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anonymous
 one year ago
The position of an object at time t is given by s(t) = 2  6t. Find the instantaneous velocity at t = 2 by finding the derivative.
anonymous
 one year ago
The position of an object at time t is given by s(t) = 2  6t. Find the instantaneous velocity at t = 2 by finding the derivative.

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Can I just plug in 2 for t?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0It says: "by finding derivative"!! Take derivative first

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.3Ok, derivative of any function f(x), (which is denoted by f'(x) ) is a [derivative]function that is the slope of f(x). And this way when you plug in a value x=a into the f'(x), you will then get the instantaneous slope (at the point on the f(x) where x=a)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.3I lost my connection for a second, apologize,

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0whatever. I don't care I'm trying to get help rn @David27

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.3The slope/derivative of a function does what? It tells you how fast a function moves. The velocity also tells you how fast a car moves (at a certain point on its position).

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.3This way, it is logical (not just because the teacher said so), that the velocity is slope of position. If velocity is slope (slope=derivative, remember) of the position, then you have to find the derivative of the postion function to find velocity

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.3You need the derivative of the positon function, to find the slopefunction (the derivative that generates the slope of the s(t) at any given point x=a), and then you need to find the slope at a particular value of x=a, that is x=2. (so plug in x=2 into the s'(t) )

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.3and hope it is clear that s'(t) is the exact v(t). Saying the the derivative of the position function , IS THE velocity function.

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.3am I typing too much? Sorry if that is the case, I can reduce wordiness

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0It's fine. I'm trying to stay with you xD

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.3Ok, so all you need is s'(2)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.3s(t) = 2  6t s'(t)=?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0That's what I need help finding id the derivative. I understand all of the stuff you posted before but this is the part that has been troubling me for ages...

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.3Oh, you just apply the rules. I can post them here in colors if you would like..

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.3I am going to use a d/dx notation to denote that I am taking the derivative and put [] around the peace the derivative of which I am taking.

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.3\(\large\color{black}{ \displaystyle \frac{d}{dx} \left[x^\color{red}{n}\right]=\color{red}{n}x^{\color{red}{n}1} }\) this is for any function where variable x is raised to a constant power of n. 

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.3Now, lets say you got a constant (a coefficient) in front of the x, what then? \(\large\color{black}{ \displaystyle \frac{d}{dx} \left[\color{blue}{c}\cdot x^\color{red}{n}\right]=\color{blue}{c}\cdot \frac{d}{dx} \left[ x^\color{red}{n}\right]=\color{blue}{c}\cdot\color{red}{n}x^{\color{red}{n}1} }\) ^ ^ ^ ^ we can take the constant c here we do the same as in the previous out, to the front like this. rule, excpet that we just multiply the whole things times this constant c. 

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.3d/dx , again, is just a notation that tells us: we are taking the derivative, and treat x as the variable (n and c, are just constants).

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.3is this still super abstruse, or is it starting to make sense?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0starting to make sense.

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.3Good. You would agree with me, if I say that the same rule applies for taking a derivative with respect to any variable. (For example, say, that instead of x, we had a "t")

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.3\(\large\color{black}{ \displaystyle \frac{d}{dt} \left[\color{blue}{c}\cdot t^\color{red}{n}\right]=\color{blue}{c}\cdot \frac{d}{dt} \left[ t^\color{red}{n}\right]=\color{blue}{c}\cdot\color{red}{n}t^{\color{red}{n}1} }\)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.3like this here, d/dt  is a notation that tells us that we treat t is a variable. and not, the same rules applies, except that we are using a different variable (not x, but t)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.3Do you know what a derivative of a constant? What is a derivative of a 2? derivative of a 4? derivative of a constant c (with respect to x)?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.3whole those i listed just now are =0.

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.3Why, because the derivative is the slope, and the slope of a line y=3, y=6, or y=c, all these lines have a slope of 0 (at any point). Therefore, when you differentiate (take a derivative) of a constant), you get 0.

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.3So lets get to our function s(t)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Ok. into the good stuff

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.3\(\large\color{black}{ \displaystyle s(t)=\underline{2}~~\underline{\color{blue}{6}\cdot t^\color{red}{1}}}\)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.3do you recongize your function s(t) ?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.3Now, take the derivative of each underlined part separately. for 2 , apply what you know about the derivative of a constant. for 6•t¹ , apply the rule that I posted (also posted below):  The rule is: \(\large\color{black}{ \displaystyle \frac{d}{dx} \left[\color{blue}{c}\cdot x^\color{red}{n}\right]=\color{blue}{c}\cdot \frac{d}{dx} \left[ x^\color{red}{n}\right]=\color{blue}{c}\cdot\color{red}{n}x^{\color{red}{n}1} }\) 

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.30 for the derivative of a 2, but the derivative of \(6t^1\) is not 0, is it?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.3\(\large\color{black}{ \displaystyle \frac{d}{dt} \left[\color{blue}{6}\cdot t^\color{red}{1}\right]=}\) please take a shot to proceed from here (if not i got your back)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.3apply the same rule, \(\large\color{black}{ \displaystyle \frac{d}{dt} \left[\color{blue}{6}\cdot t^\color{red}{1}\right]=\color{blue}{6}\cdot \frac{d}{dt} \left[ t^\color{red}{1}\right]= }\) go ahead....

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0and n would be 1, right

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.3k, will go over some basic symbols for extra, if you want to, but for now lets proceed w/ the prob

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.3So, you go 6 × 1 × t^(11)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.3(not go, but got**)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.3yes, n is 1 in this case, because your initial power is 1.

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.3So, t^(11) is same as t^0, right?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I just noticed what I did wrong and number to the 0 power is 1 not 0. That's why I got 0 and 0

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.3Oh, but this is very good, because you were able to proceed far to take the derivative already of both parts

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.3so, we had: s(t)=26t and then our derivative (or the slope, or the velocity in this case) s'(t)=06 so s'(t)=6

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.3again, derivative of s(t) (of the positon function) IS, THE VELOCITY. so your velocity function is v(t)=6

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.3then you can plug in 2 for t, (but you aren't really plugging in for t, are you?)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.3v(t)=6 there is no t to plug in for, your function is a line s(t)=6 that means that it has the same output for all values of t 9and that output is 6). That means that for any t=a, you get 6

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.3So, the velocity at t=2 is as well equal to ?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.3And that is your final answer.

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.3It is not a problem at all, you are always welcome!

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.3You can click ALT click 0, 1, 2, 5 on your number pad on the right of your keyboard release ALT it should get you ×

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.31) Click and hold ALT 2) click the number code (using the numbers that are on the right of the keyboard, and `NOT` the ones below `F1`, `F2`, `F3`, etc., ) 3) release the ALT number code result `0 2 1 5 ` × `2 4 6 ` ÷ ` 7 ` • ──────────────── among with other symbols. ` 2 5 1 ` √ `7 5 4 ` ≥ `7 5 5` ≤ `2 4 1 ` or `7 5 3` ± `2 4 7` ≈ `0 1 8 5 ` ¹ `2 5 3 ` ² 0 1 7 9 ³ ALSO, 1 6 6 ª 2 5 2 ⁿ 1 6 7 º 2 4 8 ° 0 1 9 0 ¾ 4 2 8 ¼ 1 7 1 ½ 2 2 7 π 1 5 5 ¢ 2 3 6 ∞ 1 5 9 ƒ 4 ♦ 2 5 4 ■ 2 1 9 █ 1 9 6 ─ 7 • 6 ♠ 5 ♣ 3 ♥ 13 ♪ 14 ♫ 4 8 9 Θ (there are more)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.3but this is just for symbols, if you want to get 1 tip or 2. cu
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