Question

Determine the signs (positive, negative, or zero) of y = f(x) (shown in the graph) and f^ prime x) and f^ prime prime (x) when x = 4 .

Answer 1

The graph of f is shown in the question.

At f(4), the value of the function is 0:

`f(4)=0`

This point is a local maximum point.

At the local maximum, the value of f'(x) is 0 and f''(x) < 0.

Therefore, the answers to the questions will be:

`\begin{gathered} f(4)\Rightarrow zero \\ f^(\prime)(4)\Rightarrow zero \\ f^(\prime)^(\prime)(x)\Rightarrow negative \end{gathered}`