Question

If f has a local maximum value at x = a, what would you expect the graph of f ' to look like near x = a?

The graph of f ' should be above the x-axis, cross the x-axis at x = a, and go below the x-axis as x increases.
The graph of f ' should be below the x-axis, cross the x-axis at x = a, and go above the x-axis as x increases.
The graph of f ' should be positive and increasing as x approaches a.
The graph of f ' should be negative and increasing as x approaches a.
The graph of f ' should be negative and decreasing as x approaches a.

Answer 1

The graph of f ' should be negative and decreasing as x approaches a.

Step-by-step explanation:

The graph of f ' should be negative and decreasing as x approaches a.

Answer 2

Local maximum looks like a downward U
So flip that letter U and you'll be looking at a local max.
The graph of f ' should be positive and increasing as x approaches a.