Chain Rule

 

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=?
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1 Answer

I read this as f(x)=6x²(4-4x)³. f(-2)=24(12)³=41472.

f'(x)=12x(4-4x)³+6x²(3(4-4x)²(-4))=

        12x(4-4x)³-72x²(4-4x)².

f'(-2)=(-24)(12³)-288(12²)=-82944.

So y-41472=-82944(x+2), y=-82944x-165888+41472, y=-82944x-124416.

by Top Rated User (1.2m points)

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