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

Answer 1

Well, you know it's slope will be 1. :)

The real issue is figuring out what x is when f(x) is 1. Given that, you know y=f(x), and given a point and a slope you surely know how to find the equation of a line. :)

So let us diffferentiate:

1 = f1 = 4x^3+4x.

Crumb. 4x^3+4x-1=0 doesn't seem to have any rational roots.

Is it possible you made a typo?