Question

What is the equation of the line tangent to the graph of `f(x)= x^4 + 2x^2` at the point where f ' (x)= 1?

Answer 1

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

`4x^3+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:
`root(3)(1/8+sqrt(1/64+1/27))+ root(3)(1/8-sqrt(1/64+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)`