a. Use the graph of f(x) below to estimate the value of f\'(3). is the correct a

Question

a. Use the graph of f(x) below to estimate the value of f'(3). is the correct answer 0? A. -5 B. -1 C. 0 D. 1 is the correct answer 0? A. -5 B. -1 C. 0 D. 1
graph on the bottom is for b. Idk the answer for b. b. Given the graph of f'(x), the derivative of f(x), which of the following statements are true about the graph of f(x)?
1. The graph of f does not have a point of inflection. 2. The graph of f has a point of inflection at x=2. 3. The graph of f has a critical point at x=2.
A. 1 only B. 2 only C. 3 only D. 1 and 3 only --+-+-+-+- -3 -2,-10 T5 -3 12 3 2 y

Explanation / Answer

a. Since f(x) is decreasing at x = 3, thus f '(3) will be negative

The two options remaining are -1 and -5. Since there is more change in the y direction compared to a unit change in x direction (see the boxes) therefore f '(3) < -1

Thus f '(3) = -5 option A

b. Since the f '(2) > 0 so f (x) is increasing at x = 2 but the f "(2) = 0

Therefore f has an inflection point at x=2

option B. 2 only

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