Connecting f, f', f"

The twice-differentiable function f is shown to the left on the domain (-9,9). The function f has points of inflection at x = -7.8, x = -3.6, x = 1.2, and x = 7.6. Determine what could be said about the values of f(-5), f'(-5), f"(-5).

• f(-5) < f'(-5) < f"(-5)

• f'(-5) < f(-5) < f"(-5)

• f(-5) < f"(-5) < f'(-5)

• f"(-5) < f'(-5) < f(-5)

The twice-differentiable function f is shown to the left on the domain (-9,9). The function f has points of inflection at x = -4, x = -1, x = 2.4, and x = 8. Determine what could be said about the values of f(-1), f'(-1), f"(-1).

• f"(-1) < f(-1) < f'(-1)

• f"(-1) < f'(-1) < f(-1)

• f(-1) < f"(-1) < f'(-1)

• f'(-1) < f"(-1) < f(-1)

The graph of f', the derivative of f is shown to the left. Determine the values of x, if any, at which the function f has an inflection point on the interval (-9,9).

The graph of f', the derivative of f is shown to the left. Determine all the intervals on which the function f is concave down on the interval (-9,9).

From the graph on the left it can be seen that the function f on the interval (-2,0) is positive, increasing and concave down. Based on these observations it can be concluded that:

• f' is positive and increasing, f" is negative

• f' is positive and decreasing, f" is negative

• f' is negative and decreasing, f" is negative

• f' is positive and decreasing, f" is positive

From the graph on the left it can be seen that the graph f' on the interval (5,9) is negative, decreasing and concave down. Based on these observations it can be concluded that:

• f is decreasing and concave up, f" is negative

• f is increasing and concave down, f" is positive

• f is increasing and concave down, f" is positive

• f is decreasing and concave down, f" is negative

From the graph on the left it can be seen that the graph f" on the interval (-9,-7) is positive, decreasing and concave up. Based on these observations it can be concluded that:

• f is concave up, f' is increasing

• f is increasing, f' is positive

• f is concave down, f' is decreasing

• f is concave up, f' is negative