Consider The Function F(x)=2-5x^2 On The Interval

GamaMaster0

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Consider the function f(x)=2-5x^2 on the interval [-5,4]. Find the average or mean slope of the function on this interval, i.e. f(4)-f(-5)/4-(-5)= ? By the Mean Value Theorem, we know there exists a c in the open interval (-5,4) such that f(c) is equal to this mean slope. For this problem, there is only one c that works. Find it.

 

Answer No.1

Anonymous

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Average slope = [f(4) - f(-5)]/9 = 5 f'(x) = -10x f'(c) = -10c = 5 c = -0.5

Answer No.2

Anonymous

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F(4)-f(-5)/4-(-5)= = [-78 - (-123)]/(4-(-5)) = 45/9 = 5 so c=5 then f(5) = 2 - 125 = -123

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