Expert: Ahmed Salami - 4/5/2010

Question
Can you help me to solve this problem:  Determine the interval over which F (x) = (x + 3)³ is concave upward

Answer
Hi Natalee,
A function f(x) is concave upward when its second derivative f''(x) > 0
Now,
f(x) = (x + 3)³
f'(x) = 3(x + 2)²
f''(x) = 6(x + 2)
The second derivative is zero at x = -2, and so we check the sign of the derivative on both sides of this point.
For x < -2
f''(x) < 0
For x > -2
f''(x) > 0
Our interval is therefore x > -2

Regards