Get the answer to "What is the equation of the line tangent..."

Rebekah Shelton

Answered question

2022-02-10

What is the equation of the line tangent to the graph of

f (x) = x^{4} + 2 x^{2}

at the point where f'(x)= 1?

Answer & Explanation

Sterling Mcdaniel

Beginner2022-02-11Added 10 answers

To answer this question, you'll need to solve f'(x)=1,
which is:
$4 x^{3} = 4 x = 1 .$
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:
$\sqrt[3]{\frac{1}{8} + \sqrt{\frac{1}{64} + \frac{1}{27}}} + \sqrt[3]{\frac{1}{8} - \sqrt{\frac{1}{64} + \frac{1}{27}}}$
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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