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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).
 one year ago
 one year ago
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).
 one year ago
 one year ago

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bfsgdBest ResponseYou've already chosen the best response.0
You can differentiate the function and it is increasing if f ' (x)>0.
 one year ago

onegirlBest ResponseYou've already chosen the best response.1
@electrokid can u help?
 one year ago

bfsgdBest ResponseYou've already chosen the best response.0
Differentiating f(x) we get \[f'(x)=8x^3  8x=8x(x^21)\] That is positive for all x>1.
 one year ago

bfsgdBest ResponseYou've already chosen the best response.0
No...D includes negative numbers. You need the one thats only x>1.
 one year ago

electrokidBest ResponseYou've already chosen the best response.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
 one year ago

onegirlBest ResponseYou've already chosen the best response.1
what do you mean nope?
 one year ago

electrokidBest ResponseYou've already chosen the best response.1
yep. B is not the answer
 one year ago

electrokidBest ResponseYou've already chosen the best response.1
check the interval (1,0)
 one year ago

electrokidBest ResponseYou've already chosen the best response.1
in math, there are no shortcuts. follow the "yellow brick road"
 one year ago

electrokidBest ResponseYou've already chosen the best response.1
do you see the mistake?
 one year ago

electrokidBest ResponseYou've already chosen the best response.1
so, what is the answer?
 one year ago

electrokidBest ResponseYou've already chosen the best response.1
follow the steps. did you use the number line that I drew?
 one year ago

onegirlBest ResponseYou've already chosen the best response.1
so the critical points are 1, 0 and 1
 one year ago

electrokidBest ResponseYou've already chosen the best response.1
sorry. yes. you are correct. "3" points, 1, 0 and 1
 one year ago

electrokidBest ResponseYou've already chosen the best response.1
dw:1364919097503:dw
 one year ago

electrokidBest ResponseYou've already chosen the best response.1
interval (inf, 1) plug in x=2 and find f'(x)
 one year ago

onegirlBest ResponseYou've already chosen the best response.1
plug in 2 into the problem?
 one year ago

electrokidBest ResponseYou've already chosen the best response.1
into the entire thing f'(x)
 one year ago

onegirlBest ResponseYou've already chosen the best response.1
and the derivative i got 0
 one year ago

electrokidBest ResponseYou've already chosen the best response.1
\[f'(2)=8(2)[(2)^21]=?\]
 one year ago

electrokidBest ResponseYou've already chosen the best response.1
good.dw:1364919435696:dw now, we check interval (1,0) find \[f'(0.5)\]
 one year ago

onegirlBest ResponseYou've already chosen the best response.1
you mean find the derivative of 0.5 ?
 one year ago

electrokidBest ResponseYou've already chosen the best response.1
derivative "at" x=0.5
 one year ago

electrokidBest ResponseYou've already chosen the best response.1
yep. what did you get?
 one year ago

onegirlBest ResponseYou've already chosen the best response.1
i'm still getting 0 :/
 one year ago

electrokidBest ResponseYou've already chosen the best response.1
\[f'(0.5)=8(0.5)[(0.5)^21]=?\]
 one year ago

electrokidBest ResponseYou've already chosen the best response.1
good.dw:1364919843444:dw now we check interval (0,1) lets take x = 0.5 similarly, find \[f'(0.5)\]
 one year ago

electrokidBest ResponseYou've already chosen the best response.1
great dw:1364919912982:dw now the final interval (1,+infty) we take x= 2 \[f'(2)=?\]
 one year ago

electrokidBest ResponseYou've already chosen the best response.1
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)
 one year ago

electrokidBest ResponseYou've already chosen the best response.1
so, in what intervals do you see f'(x) positive?
 one year ago

onegirlBest ResponseYou've already chosen the best response.1
ok in 0,1 and 1, + infi
 one year ago

electrokidBest ResponseYou've already chosen the best response.1
great. which option says that?
 one year ago

electrokidBest ResponseYou've already chosen the best response.1
and that is your answer yay
 one year ago

electrokidBest ResponseYou've already chosen the best response.1
follow the same procedure for the other one,
 one year ago
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