Consider the function f(x)=1x^2+5x+8 on the interval [-2,5]

Question

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

(f(5)-f(-2))/(5-(-2))=_______

By the Mean Value Theorem, we know there exists a c in the open interval (-2,5) such that f'(c) is equal to this mean slope. For this problem, there is only one c that works. c=____

Answer 1

f'(c) = 2c + 5 = (f(5) -f(-2))/ (5 - -2) 2 c + 5 = (58 -2)/7 = 56/7 = 8 so 2 c +5 = 8 2 c =3 and c= 3/2 which is in the interval (-2,5)