Below is the graph of f \'(x), the derivative of f(x), and has x-intercepts at x

Question

Below is the graph of f '(x), the derivative of f(x), and has x-intercepts at x = -3, x = 1 and x = 2. There are horizontal tangents at x = -1.5 and x = 1.5. Which of the following statements is true?

Below is the graph of f '(x), the derivative of f(x), and has x-intercepts at x = -3, x = 1 and x = 2. There are horizontal tangents at x = -1.5 and x = 1.5. Which of the following statements is true?

(

f is decreasing from x = -1.5 to x = 1.5. f is concave up from x = 2 to x = 3. f has a relative maximum at x = -3. None of these is true. (-1/5, 13 1) +11 -3.2 -2.4 -1.6 -8.8 0.8 1.6 / 2.4 3.2 1.5, -1.1)

Explanation / Answer

Clearly , as this is the graph of f'(x) , so its slope will give the value of f''(x).

And this slope derermines concavity of the function.

Here in the interval (2,3) ,the slope of graph is positive.

So it will be concave up from x=2 to x=3.

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