
New Member
Concave Down and Increasing?
On which interval is the graph of f(x)=4x^(3/2)  3x^2 both concave down and increasing?
A. (0,1) B. (0, .5) C. (0, .25) D. (.25, .5) E. (.25, 1)
I found f'(x)=6x^1/2  6x
and f''(x)=3x^1/2  6
I set f'' equal to zero and got x=.25
Also, I believe it is undefined at 0?
Would the answer be C? I'm not sure where to go from here if it's not.

Elite Member
A function, f, is increasing as long as f' is positive and is concave down where f'' is negative.
You want an interval where [tex]6x^{1/2} 6x> 0[/tex] and [tex]3x^{1/2} 6< 0[/tex].
Last edited by HallsofIvy; 10152014 at 08:01 PM.

New Member
The answer is (0, .25), correct?
f' is positive below 1 and f'' is negative below .25, so they both overlap in (0, .25)
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