Graph Derivative Problem

[Jason76]

Where are the 1st and 2nd derivatives both negative? Answer: B Why

 

[mathmari]

If the first derivative \(\displaystyle f' \) is negative, then the function \(\displaystyle f \) is decreasing.
If the second derivative \(\displaystyle f'' \) is negative, then the function \(\displaystyle f \) is concave down.

 

[DrPhil]

Where are the 1st and 2nd derivatives both negative? Answer: B Why

View attachment 3128

B and C are the only named points at which the 1st derivative is negative.
At point C, the curve is clearly concave up, so 2nd derivative is not negative.
Point B is not so clear, but I would have said it is concave down, so B is the only point with both 1st and 2nd derivatives negative.