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Consider the function f(x) = 6 - 8x2 on the interval [-4, 7]. Find the average or mean slope of the function on this interval, i.e. f(7) - f(-4)/7 - (-4) = By the Mean Value Theorem, we know there exists a C in the open interval (-4, 7) such that f'(c) is equal to this mean slope. For this problem, there is only one c that works. Find it. Consider the function f(x) = 1/x on the interval [1, 12]. Find the average or mean slope of the function on this interval. By the Mean Value Theorem, we know there exists a c in the open interval (1, 12) such that f'(c) is equal to this mean slope. For this problem, there is only one c that works. Find it.
Show transcribed image text Consider the function f(x) = 6 - 8x2 on the interval [-4, 7]. Find the average or mean slope of the function on this interval, i.e. f(7) - f(-4)/7 - (-4) = By the Mean Value Theorem, we know there exists a C in the open interval (-4, 7) such that f'(c) is equal to this mean slope. For this problem, there is only one c that works. Find it. Consider the function f(x) = 1/x on the interval [1, 12]. Find the average or mean slope of the function on this interval. By the Mean Value Theorem, we know there exists a c in the open interval (1, 12) such that f'(c) is equal to this mean slope. For this problem, there is only one c that works. Find it.