For f(x)=-\frac{x}{3} what is the equation of the tangent line

Erik Sears

Erik Sears

Answered question

2022-02-16

For f(x)=x3 what is the equation of the tangent line at x=-3?

Answer & Explanation

razlikaml42

razlikaml42

Beginner2022-02-17Added 5 answers

First we need to find the slope at the given point so we take the derivative of f(x):
ddx[f(x)=x3]f(x)=13
This tells us the slope is 13 at any given point, now that we have a slope we need to find a point. The question tells us our x value is -3 so plugging that value into f(x) gives us 1.
So our point is (-3, 1) and our slope is 13 now we can put this into slope point from which is:
yy1=m(xx1) where m is slope and (x1,y1)
Plugging all values gives us:
y1=13(x(3)) which is also y=x3, we get the original equation because the graph is linear and so the function can represent the value at any given point since the slope does not change

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