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anonymous
 one year ago
Find an equation of the tangent line to the graph f(x)=27x^2 at (2,26)
anonymous
 one year ago
Find an equation of the tangent line to the graph f(x)=27x^2 at (2,26)

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amistre64
 one year ago
Best ResponseYou've already chosen the best response.2what are 2 things we need to know to define a line?

amistre64
 one year ago
Best ResponseYou've already chosen the best response.2well, 2 points are useful yes, but we only have one point given to us ... what else could we use to define a line with? a point and ....

amistre64
 one year ago
Best ResponseYou've already chosen the best response.2correct, so a point and a slope can be used to define a line. its called the point slope form of the equation. now, how do we determine the slope of a curve at a given point?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0the change in y over the change in x? so the point slope equation?

amistre64
 one year ago
Best ResponseYou've already chosen the best response.2hmm, im assuming you know what a derivative is for this to work.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yeah but I don't really get derivatives

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I know there's 4 types

amistre64
 one year ago
Best ResponseYou've already chosen the best response.2you should have a simple rule you can apply constant rule, and a power rule

amistre64
 one year ago
Best ResponseYou've already chosen the best response.2\[\frac{d}{dx}k=0\] \[\frac{d}{dx}x^n=n~x^{n1}\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I'm just having a hard time applying the equation to these rules

amistre64
 one year ago
Best ResponseYou've already chosen the best response.29  x^2 ^ ^ ^ this is a power of x ^ and this is a constant

amistre64
 one year ago
Best ResponseYou've already chosen the best response.2what is the derivative of 9? what is the derivative of x^2?

amistre64
 one year ago
Best ResponseYou've already chosen the best response.2e3rr, 7x^2 ... forgot the equation we were dealing with :/

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so for 2 it would be 0 and 7x^2 would be 7x^6?

amistre64
 one year ago
Best ResponseYou've already chosen the best response.2\[\frac{d}{dx}(27x^2)\] \[\frac{d}{dx}(29)\frac{d}{dx}(7x^2)\] \[\frac{d}{dx}(2)7\frac{d}{dx}(x^2)\] \[07(2x^{21})\]

amistre64
 one year ago
Best ResponseYou've already chosen the best response.2typo, slip of the fingers.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0can you please explain how you got the answer step by step?

amistre64
 one year ago
Best ResponseYou've already chosen the best response.2i jsut did ... except for 29 which is spose to be a 2 instead use the constant rule for the constant, and the power rule for the power of x there is also a 'pull out' rule which lets us pull out that 7 to the outside.

amistre64
 one year ago
Best ResponseYou've already chosen the best response.2your 7x^2 derivative is off ... try it again

amistre64
 one year ago
Best ResponseYou've already chosen the best response.2the format for the tangent line is just gonna be: y  f(a) = f'(a) (xa) so as long as we can determine f'(a) we are set

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0sorry my book shows different explanations so I'm a little confused right now

amistre64
 one year ago
Best ResponseYou've already chosen the best response.2tell me your thoughts then, what does your book explain?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0it basically shows me all these rules but all these variables are confusing me

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0but the examples only show me if I have a point and slope

amistre64
 one year ago
Best ResponseYou've already chosen the best response.2what is your rule for powers of x?

amistre64
 one year ago
Best ResponseYou've already chosen the best response.2can you take a picture of it?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0For any real number k if y=x^k then d/dx(x^h)= k*x^k1

amistre64
 one year ago
Best ResponseYou've already chosen the best response.2let k=2 x^2 become 2x^(21) or simply 2x

amistre64
 one year ago
Best ResponseYou've already chosen the best response.2so our derivative is 7x^2 derives to 7(2x), at x=2 that is ... 7(4)

amistre64
 one year ago
Best ResponseYou've already chosen the best response.2out point (2,26) defines the value of x as 2

amistre64
 one year ago
Best ResponseYou've already chosen the best response.22x, when x=2 is just ... 2(2) right?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0how did x^2 become 2x?

amistre64
 one year ago
Best ResponseYou've already chosen the best response.2by the derivative rule you posted. let k=2

amistre64
 one year ago
Best ResponseYou've already chosen the best response.2x^k derives to k*x^(k1)

amistre64
 one year ago
Best ResponseYou've already chosen the best response.2by first principles of limit \[\lim_{h\to0}\frac{(x+h)^2x^2}{(x+h)x}\] \[\lim_{h\to0}\frac{x^2+h^2+2xhx^2}{h}\] \[\lim_{h\to0}\frac{h^2+2xh}{h}\] \[\lim_{h\to0}\frac{h(h+2x)}{h}\] \[\lim_{h\to0}(h+2x)=2x\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0but I'm still pretty confused

amistre64
 one year ago
Best ResponseYou've already chosen the best response.2the 'rules' are really a table of outcomes that can be applied so that you dont have to use the long limiting process each and every time.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so now that we know the derivative of 7x^2 to be 7(2x) which is 7(2*2)= 28 what do we do next?

amistre64
 one year ago
Best ResponseYou've already chosen the best response.2well, thats our slope of our tangent line. the rest is from algebra class.

amistre64
 one year ago
Best ResponseYou've already chosen the best response.2construct the line using your slope and the stated point

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0or point slope equation yy1=m(xx1)

amistre64
 one year ago
Best ResponseYou've already chosen the best response.2y  f(a) = f'(a) (xa) or rewritten as y = f'(a) (xa) +f(a)

amistre64
 one year ago
Best ResponseYou've already chosen the best response.2point slope equation

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0could I get a two out of it to be 2(14x+15)? or is okay like that?

amistre64
 one year ago
Best ResponseYou've already chosen the best response.2usually we dont factor it, keep it in y=mx+b form is conventional

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so that's my final answer? thank you! is there any way I reward you on here? it's my first time using this site

amistre64
 one year ago
Best ResponseYou've already chosen the best response.2there should be a 'best response' button to everything ive posted. clicking it gives out a medal. but saying thank you and learning a little bit is reward enough for me to be honest.

amistre64
 one year ago
Best ResponseYou've already chosen the best response.2youre welcome :) and good luck
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