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.

Question

Mathematics

Aracely Jefferson

19 March, 16:45

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.

+3

Answers (1)

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Long · Answer 1

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.