Average slope and find C

Question

Consider the function f(x) =4sqrtx+2  on the interval [ 1 , 6 ]. 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 , 6 ) such that f'( c) is equal to this mean slope. For this problem, there is only one c that works. Find it.

Answer 1

f'(x) = 2/√x

 

f'(c) = [f(6) - f(1)]/(6 - 1) = [4√6 + 2 - 4√1 - 2]/5 = 4(√6 - 1)/5 = 2/√c

 

c = 5/[2(√6 - 1)] = 1.72