Question

find the value(s) of c that satisfy the (f(b) - f(a))/b-a = f'(c) in the conclusion of the mean value theorem for the function and interval. f(x) = x^2 + 5x + 2, [1, 2]

Answer 1

so you want the slope of the line that runs between your interval ends (1,2) then find the point that that slope touches only once.

Answer 2

In other words you need to find two things: the slope between 2 points and the derivative of the function f(x).
f'(x) = f(2) - f(1)/(2-1)
solve for x