Consider the function f(x) = 1 -4x on the interval [-3, 8]. (A) Find the average or mean slope of the function on this interval, i.e. f(8) - f(-3) 8 - (-3) (B) By the Mean Value Theorem, we know there exists a c in the open interval (-3, 8) such that f'(c) is equal to this mean slope. For this problem, there is only one c that works. Find it. C =Consider the function graphed below. a n p b Does this function satisfy the hypotheses of the Mean Value Theorem on the interval [a, b]? ? v Does it satisfy the conclusion? |? At what point c is f'(c) _ f(6) - f(a). b - a ? VLet f() = 2x2 + 4x - 10. Answer the following questions. 1. Find the average slope of the function f on the interval [-1, 1]. Average Slope: m = 2. Verify the Mean Value Theorem by finding a number c in (-1, 1) such that f (c) = m. Answer: c =Consider the function m) : 50:3 7 3.70 on the interval [ 4, 4]. (A) Find the average or mean slope of the function on this interval. Average Slope : '3 (B) By the Mean Value Theorem, we know there exists at least one c in the open interval (4,4) such that f'(c) is equal to this mean slope. Find all values of c that work and list them (separated by commas) in the box below. List of values: [I Consider the function f(x) = 2\ + 10 on the interval [3, 6]. (A) Find the average or mean slope of the function on this interval. Average Slope = (B) By the Mean Value Theorem, we know there exists at least one c in the open interval (3, 6) such that f'(c) is equal to this mean slope. Find all values of c that work and list them (separated by commas) in the box below. List of values:At 2:00pm a car's speedometer reads 20mph, and at 2:10pm it reads 25mph. Use the Mean Value Theorem to find an acceleration the car must achieve. Answer( in mi/h2):]