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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).

Mathematics
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You can differentiate the function and it is increasing if f ' (x)>0.
huh?
@electrokid can u help?

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Other answers:

Differentiating f(x) we get \[f'(x)=8x^3 - 8x=8x(x^2-1)\] That is positive for all x>1.
ok
so what do i do next?
That's it :)
ohh so it will be D?
No...D includes negative numbers. You need the one thats only x>1.
|dw:1364917996121:dw| get the critical points you see the four intervals? take an arbitrary number from each interval and check the signs of the derivative
Ohh so its B
Yep :)
nope
what do you mean nope?
so its wrong?
Its right....
yep. B is not the answer
check the interval (-1,0)
in math, there are no shortcuts. follow the "yellow brick road"
ok
do you see the mistake?
yea
so, what is the answer?
i got C
follow the steps. did you use the number line that I drew?
yea hold on
so the critical points are -1, 0 and 1
okay
sorry. yes. you are correct. "3" points, -1, 0 and 1
lol ok
|dw:1364919097503:dw|
interval (-inf, -1) plug in x=-2 and find f'(x)
plug in -2 into the problem?
yep
into (x - 2)^2?
into the entire thing f'(x)
ok
idk i got 16?
and the derivative i got 0
\[f'(-2)=8(-2)[(-2)^2-1]=?\]
ohh i got -48
good.|dw:1364919435696:dw| now, we check interval (-1,0) find \[f'(-0.5)\]
okay i get 0
nope try again.
you mean find the derivative of -0.5 ?
derivative "at" x=-0.5
ohhh ok
yep. what did you get?
i'm still getting 0 :/
\[f'(-0.5)=8(-0.5)[(-0.5)^2-1]=?\]
ok i get 3
good.|dw:1364919843444:dw| now we check interval (0,1) lets take x = 0.5 similarly, find \[f'(0.5)\]
okay
i get -3
great |dw:1364919912982:dw| now the final interval (1,+infty) we take x= 2 \[f'(2)=?\]
ok i get 48
perfect. |dw:1364919991818:dw| now, f(x) is increasing when f'(x) >0 (i.e., f'(x) is positive) and f(x) is decreasing when f'(x) < 0 (i.e., f'(x) is negative)
so, in what intervals do you see f'(x) positive?
ok in 0,1 and 1, + infi
great. which option says that?
A!
and that is your answer yay
thanks :)
follow the same procedure for the other one,
ok

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