2nd Derivative Test

A function has critical points at x=-2 and x=4. Using the graph of f’’(x) below, determine whether each critical point is a local max, local min, or neither. : 

A function has critical points at x=-2 and x=4. Using the graph of f’’(x) below, determine whether each critical point is a local max, local min, or neither. What does the 2nd Derivative test say? A critical point is a local max if f’’(x) is negative (the function is concave down) A critical point is a local min if f’’(x) is positive (the function is concave up) @ x=-2, f’’(x) is positive. This means the function has a local min! @ x=4, f’’(x) is negative. This means the function has a local max!