# For what values of x is #f(x)= (x-x^3)/(2-x^3)# concave or convex?

##### 1 Answer

Aug 1, 2016

f(x) is concave down in (0,

&

concave up in (0,

#### Explanation:

f'' (x) would be

For concavity, the second derivative test says that for f(x) is concave up for that value of x for which f''(x)>0 and concave down if f''(x)<0.

From the 2nd derivative shown above, it can be ascertained that for x>0 and up to x<

Hence f(x) is concave down in (0,

Like wise for all x<0, f''(x) would be positive and hence concave up.