What is the equation of the line tangent to the

Rebekah Shelton 2022-02-10 Answered
What is the equation of the line tangent to the graph of f(x)=x4+2x2 at the point where f'(x)= 1?
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Expert Answer

Sterling Mcdaniel
Answered 2022-02-11 Author has 10 answers

To answer this question, you'll need to solve f'(x)=1,
which is:
4x3=4x=1.
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:
18+164+1273+18164+1273
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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