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onegirl
 2 years 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).
onegirl
 2 years 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).

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bfsgd
 2 years ago
Best ResponseYou've already chosen the best response.0You can differentiate the function and it is increasing if f ' (x)>0.

onegirl
 2 years ago
Best ResponseYou've already chosen the best response.1@electrokid can u help?

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

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

electrokid
 2 years ago
Best ResponseYou've already chosen the best response.1dw: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

electrokid
 2 years ago
Best ResponseYou've already chosen the best response.1yep. B is not the answer

electrokid
 2 years ago
Best ResponseYou've already chosen the best response.1check the interval (1,0)

electrokid
 2 years ago
Best ResponseYou've already chosen the best response.1in math, there are no shortcuts. follow the "yellow brick road"

electrokid
 2 years ago
Best ResponseYou've already chosen the best response.1do you see the mistake?

electrokid
 2 years ago
Best ResponseYou've already chosen the best response.1so, what is the answer?

electrokid
 2 years ago
Best ResponseYou've already chosen the best response.1follow the steps. did you use the number line that I drew?

onegirl
 2 years ago
Best ResponseYou've already chosen the best response.1so the critical points are 1, 0 and 1

electrokid
 2 years ago
Best ResponseYou've already chosen the best response.1sorry. yes. you are correct. "3" points, 1, 0 and 1

electrokid
 2 years ago
Best ResponseYou've already chosen the best response.1dw:1364919097503:dw

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

onegirl
 2 years ago
Best ResponseYou've already chosen the best response.1plug in 2 into the problem?

electrokid
 2 years ago
Best ResponseYou've already chosen the best response.1into the entire thing f'(x)

onegirl
 2 years ago
Best ResponseYou've already chosen the best response.1and the derivative i got 0

electrokid
 2 years ago
Best ResponseYou've already chosen the best response.1\[f'(2)=8(2)[(2)^21]=?\]

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

onegirl
 2 years ago
Best ResponseYou've already chosen the best response.1you mean find the derivative of 0.5 ?

electrokid
 2 years ago
Best ResponseYou've already chosen the best response.1derivative "at" x=0.5

electrokid
 2 years ago
Best ResponseYou've already chosen the best response.1yep. what did you get?

electrokid
 2 years ago
Best ResponseYou've already chosen the best response.1\[f'(0.5)=8(0.5)[(0.5)^21]=?\]

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

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

electrokid
 2 years ago
Best ResponseYou've already chosen the best response.1perfect. 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)

electrokid
 2 years ago
Best ResponseYou've already chosen the best response.1so, in what intervals do you see f'(x) positive?

onegirl
 2 years ago
Best ResponseYou've already chosen the best response.1ok in 0,1 and 1, + infi

electrokid
 2 years ago
Best ResponseYou've already chosen the best response.1great. which option says that?

electrokid
 2 years ago
Best ResponseYou've already chosen the best response.1and that is your answer yay

electrokid
 2 years ago
Best ResponseYou've already chosen the best response.1follow the same procedure for the other one,
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