Rebekah Shelton
2022-02-10
Answered

What is the equation of the line tangent to the graph of $f\left(x\right)={x}^{4}+2{x}^{2}$ at the point where f'(x)= 1?

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Sterling Mcdaniel

Answered 2022-02-11
Author has **10** answers

To answer this question, you'll need to solve f'(x)=1,

which is:

This equation has no rational solution, so you'll need to approximate, by some method either technological or otherwise. (Or use the general formula for the solution of a cubic to get:

Once you get an approximation, call it a, find f(a) to get the point: (a, f(a)) on the curve. And, since f'(a)=1, we get:

The equation of the tangent line is:

y=x-a+f(a)

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