Find the average of mean slope of the function and the c that exists

Question

Consider the function f(x)=2√(x)+1 on the interval [2,7]. Find the average of mean slope of the function on this interval. (Provide specific answers)

By the mean value theorem, we know there exists a c in the open interval (2,7) such that f prime (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)+1

f(7) = 2√7 + 1

f(2) = 2√2 + 1

mean slope is (f(7) - f(2))/5 = 0.4926

f'(x) = (1/√x)

1/√(x) = 0.4926

x= 4.1210