Question

What are the critical values, if any, of `f(x) = 2x^4 - 4x^2 +6`?

Answer 1

critical values at `x = 0, x = +- 1`

Explanation:

Given: `f(x) = 2x^4 - 4x^2 + 6`

Find the first derivative:

`f'(x) = 8x^3 - 8x`

Find critical values by factoring and setting `f'(x) = 0`:

`f'(x) = 8x^3 - 8x = 8x(x^2 - 1) = 8x (x+1)(x-1) = 0`

critical values at `x = 0, x = +- 1`

Graph of `f(x) = 2x^4 - 4x^2 + 6`:

graph{2x^4 - 4x^2 + 6 [-5, 5, -2, 10]}