# For what values of x is #f(x)=3x^3-7x^2-5x+9# concave or convex?

##### 1 Answer

Jun 5, 2016

#### Explanation:

The convexity and concavity of the function

- If
#f''>0# , then#f# is convex. - If
#f''<0# , then#f# is concave.

To find the function's second derivative, use the power rule.

#f(x)=3x^3-7x^2-5x+9#

#f'(x)=9x^2-14x-5#

#f''(x)=18x-14#

So, the convexity and concavity are determined by the sign of

The second derivative equals

When

When