D Question 5 4 pts The function f(x) = x2 – 4x satisfies the hypotheses of the Mean Value Theorem on the interval (-1,1]. Find the value of c that satisfies the conclusion of the Mean Value Theorem on the interval (-1,1]. Write your answer as a numerical value in simplest form. Question 1 4 pts Suppose that f and g are differentiable functions such that f(x) = ln(g(x)). If g(3) = 5 and g (3) = 30, what is f'(3)? Write your answer as a numerical value in simplest form. Question 2 4 pts Suppose that when a pebble is dropped into a calm pond, it causes ripples in the form of concentric circles. Suppose that the radius of the outer ripple of the disturbed water is increasing at a rate of 1 meter per second. At what rate is the area of the disturbed water changing (in square meters per second) when the radius is 3 meters? 27 370 1 97 O 67 Question 3 4 pts Let f(x) = x + 2/2 Which of the following represents the linearization of f at a = 1? = L(x) = 3 + 2(x – 1) OL(x) = 2 + 3(x + 1) O L(x) = 2 + 3(x – 1) OL(x) = 3+2(x+1) Question 4 4 pts = Which of the following are critical numbers of the function f(x) = x4 – 2×2 + 5 ? Select all that apply. -1 0 0 4 0
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