Need help solving this..

Question

Suppose f(−2)=5 ,f'(−2)=0, and f''(−2)=−3.

What can we say about the point (-2, 5)?

Answer 1

There is a horizontal tangent line at (-2,5) because the first derivative has a value of zero. Since the 2nd derivative is negative at that point, there is a relative maximum there. Think 2nd derivative negative, concave downward (negative means frown-∩-concave down), so the horizontal tangent line is above the curve.