Question

For what intervals is f(x) = 2x^4 – 4x^2 + 6 increasing?

A. The graph is increasing on the intervals (-1, 0) and (1, ∞).
B. The graph is increasing on the interval (1, ∞).
C. The graph is increasing on the interval (-1, 0).
D. The graph is increasing on the intervals ( -∞ , -1) and (0, 1).

Answer 1

You can differentiate the function and it is increasing if f ' (x)>0.

Answer 2

huh?

Answer 3

@electrokid can u help?

Answer 4

Differentiating f(x) we get \[f'(x)=8x^3 - 8x=8x(x^2-1)\] That is positive for all x>1.

Answer 5

ok

Answer 6

so what do i do next?

Answer 7

That's it :)

Answer 8

ohh so it will be D?

Answer 9

No...D includes negative numbers. You need the one thats only x>1.

Answer 10

get the critical points
you see the four intervals?
take an arbitrary number from each interval and check the signs of the derivative