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Chain Rule

0 votes

Suppose that

f(x)=6x^2(4−4x)^3

Find an equation for the tangent line to the graph of f at x=−2, y=?
asked Feb 26, 2014 in CALCULUS by payton Apprentice

1 Answer

0 votes

The function

The derivative at a point of a function of a single variable gives the slope of the tangent line

to the graph of the function at that point.

The line having this slope and passes through the point at image gives the tangent line to f(x).

Now find the derivative of .

image

image

Apply the formula image

Let image.

image

image

image

At image,

image

image

image

image

This is the slope of the tangent line image.

Now find the point on tangent line at image.

image

image

image

Equation of line through the point image and having slope m is image.

So, the line through the point image and having slope image is

image

image

image

image

image

This is the tangent line.

The tangent line of the function is image.

The value of y at image is 41472.

The graph with tangent line is

answered Apr 19, 2014 by Johncena Apprentice

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