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thuyvy
 3 years ago
Find equations of all tangents to the curve f(x)=9/x that have slope 1
thuyvy
 3 years ago
Find equations of all tangents to the curve f(x)=9/x that have slope 1

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ivanmlerner
 3 years ago
Best ResponseYou've already chosen the best response.0At first you have to take the derivative of f. Do you understand why is that?

ivanmlerner
 3 years ago
Best ResponseYou've already chosen the best response.0Ok, now what is the meaning of the derivative? Knowing this meaning can you guess what the next step would be?

thuyvy
 3 years ago
Best ResponseYou've already chosen the best response.0that is when a function change as the input change, but I'm stuck at the 2nd step what shall I do next? plug in 1 slope as x?

ivanmlerner
 3 years ago
Best ResponseYou've already chosen the best response.0Yes, in other words it is the rate of change of a function. But the meaning I was thinking of is the same, but a little diferent. When the input increases in a really small amount, the value changes too. Since those two changes are very small, the rate of change is approximately the change in the value divided by the increase in the input. Do you understand what I just said?

thuyvy
 3 years ago
Best ResponseYou've already chosen the best response.0not really, can you lead me into solving this? what is the second step I should take?

ivanmlerner
 3 years ago
Best ResponseYou've already chosen the best response.0You need to understand it before gettingg to the next step. But if you want to know, the derivative of a function at x is the slope of its tangent line at this point, that was what I was trying to show you. Then, you should put 9/x2=1, that is the slope, to find in which points the line passes.

thuyvy
 3 years ago
Best ResponseYou've already chosen the best response.0Yes I got to this step, when I was trying to solve for x I got + 3

thuyvy
 3 years ago
Best ResponseYou've already chosen the best response.0but the answer that it should be is y=x6 and y = x+6

thuyvy
 3 years ago
Best ResponseYou've already chosen the best response.0so I must have done something wrong right?

ivanmlerner
 3 years ago
Best ResponseYou've already chosen the best response.0Wait, you just found out one point in wich the line passes, it is not the answer yet

ivanmlerner
 3 years ago
Best ResponseYou've already chosen the best response.0What you did so far is correct

thuyvy
 3 years ago
Best ResponseYou've already chosen the best response.0oh ic okay, so the other point is 3 since 9/x = y and x is 3 therefore y = 3 right?

ivanmlerner
 3 years ago
Best ResponseYou've already chosen the best response.0or 3, but yes, thats correct

ivanmlerner
 3 years ago
Best ResponseYou've already chosen the best response.0Now, you know a point that belongs to the line, and its slope. The general formula for a line is y=ax+b, and you alrady have a, now put the point you know that belongs to it, and you will find b.

FaisalAyaz
 3 years ago
Best ResponseYou've already chosen the best response.0use slope intercept form now

thuyvy
 3 years ago
Best ResponseYou've already chosen the best response.0sorry, I'm kinda slow at this point, how do I set this = to 9?

ivanmlerner
 3 years ago
Best ResponseYou've already chosen the best response.0You dont need to, you know x and y, from the points (3, 3) and (3, 3) that this tangent passes through, and you know a. Now: 3=1*(3)+b1 3=1*3+b2

ivanmlerner
 3 years ago
Best ResponseYou've already chosen the best response.0Before, you found out in which points the tangent have this slope, then, you found out the value of the function at this point, and now you use those information to get the formulas for the tangent lines. You seem a little bit confused with what the numbers you are getting mean.

thuyvy
 3 years ago
Best ResponseYou've already chosen the best response.0I got it thanks so much for being so patience :)

thuyvy
 3 years ago
Best ResponseYou've already chosen the best response.0can I ask you something else?

thuyvy
 3 years ago
Best ResponseYou've already chosen the best response.0same type of problem but it's f(x) = square root of (x+9)

thuyvy
 3 years ago
Best ResponseYou've already chosen the best response.0slope 1/2 I did the derivatives and solve for x I got x= 1

thuyvy
 3 years ago
Best ResponseYou've already chosen the best response.0I plugged x= 1 back to original equation I got y = +/ 2 sqrt 2 then I use slope intercept to find equations, I got y= 1/4+9/4 sqrt 2

thuyvy
 3 years ago
Best ResponseYou've already chosen the best response.0but the answer should be y=1/4+13/4 where did I do wrong?

ivanmlerner
 3 years ago
Best ResponseYou've already chosen the best response.0You got the x wrong.

thuyvy
 3 years ago
Best ResponseYou've already chosen the best response.0original fx is sqrt(x=9) derivative is 1/2(x+9)^1/2

ivanmlerner
 3 years ago
Best ResponseYou've already chosen the best response.0its (1/2)(x+9)^(1/2)

thuyvy
 3 years ago
Best ResponseYou've already chosen the best response.0Yes i got that.. But solving for x=1

ivanmlerner
 3 years ago
Best ResponseYou've already chosen the best response.0Well, thats wrong, did you see the minus, in the exponent?

thuyvy
 3 years ago
Best ResponseYou've already chosen the best response.0No i said that mine is 1/{2(x+9)^1/2 same thing

ivanmlerner
 3 years ago
Best ResponseYou've already chosen the best response.0\[\frac{ 1 }{ 2 }=\frac{ 1 }{ 2\sqrt{x+9} }\rightarrow \sqrt{x+9}=1\rightarrow x+9=\pm1\rightarrow x=10 or 8\]

thuyvy
 3 years ago
Best ResponseYou've already chosen the best response.0the slope is 1/4 not 1/2

ivanmlerner
 3 years ago
Best ResponseYou've already chosen the best response.0sorry, didnt ssee you posting. Then the left side of the equation will be 1/4, and sqrt(x+9)=2 and x+9=+4, wich gives us: x=5, and x=13

ivanmlerner
 3 years ago
Best ResponseYou've already chosen the best response.0Can you go from there?

thuyvy
 3 years ago
Best ResponseYou've already chosen the best response.0let me try to do calculation, I did the calculation but got +/ 2 sqrt 2.. give me 1 minute please

thuyvy
 3 years ago
Best ResponseYou've already chosen the best response.0I got it, I think I got messed up when I was trying to square to get rid of sq rt. Thanks Do you have time to help me on other problems?

ivanmlerner
 3 years ago
Best ResponseYou've already chosen the best response.0I'm almost leaving actually, but I'm here almost every day.

thuyvy
 3 years ago
Best ResponseYou've already chosen the best response.0quick question on solving this problem \[z(4z+7)  x(4x+7) / (zx)\]

thuyvy
 3 years ago
Best ResponseYou've already chosen the best response.0I can combine (zx) then cancel top and bottom right?

thuyvy
 3 years ago
Best ResponseYou've already chosen the best response.0so what is have left is (4z+7) * (4x+7) right?

ivanmlerner
 3 years ago
Best ResponseYou've already chosen the best response.0No, be carefull, think of what is being divided, when you have something that is not being divided you cannot sum them withou a common denominator

thuyvy
 3 years ago
Best ResponseYou've already chosen the best response.0oh maybe that's why. thanks
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