# Thread: Concave Down and Increasing?

1. ## 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.

2. A function, f, is increasing as long as f' is positive and is concave down where f'' is negative.
You want an interval where $6x^{1/2}- 6x> 0$ and $3x^{-1/2}- 6< 0$.

3. The answer is (0, .25), correct?

f' is positive below 1 and f'' is negative below .25, so they both overlap in (0, .25)