Find the average or mean slope of the function on this interval.

Question

Consider the function f(x)=3x³-5x on the interval [-5,5]. Find the average or mean slope of the function on this interval. 

By the mean value theorem, we know there exists at least one c in the open interval (-5,5) such that f^'(c) is equal to this mean slope. For this problem, there are two values of c that work.

the smaller value is?

the larger value is?

 

Answer 1

f'(c) =[ f(b) - f(a)]/(b - a) = (350 + 350)/(5 + 5) = 700/10 = 70

 

f'(c) = 70

 

f'(x) = 9x^2 - 5

 

9c^2 - 5 = 70

 

9c^2 = 75

 

c^2 = 75/9

 

c = +/- (5/3)(3)^.5

Answer 2

Francisco E. Answered this yesterday.check back for his explanation.