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.