Find the intervals which f is concave down.

Question

f(x)=10–12x+6x²–x³

 

Answer 1

A function is concave down on intervals where the 2nd derivative is negative.  

 

f'(x) = -12 + 12x - 3x²

f''(x) = 12 - 6x

 

f''(x) < 0  

12 - 6x < 0

6x > 12

x > 2

 

f is concave down on (2,∞)