Find the value or values of c that satisfy the equation fbfa

Find the value or values of c that satisfy the equation f(b)-f(a)/b-a=f\'(c) in the conclusion of the Mean Value Theorem for the following function and interval. f(x) = 5x2 + 2x - 3, [-3,-1] The value(s) of c that satisfy the equation f(b)-f(a)/b-a=f\'(c) is/are . (Type a simplified fraction. Use a comma to separate answers as needed.)

Solution

f\'= 10x +2 f(b) -f(a)/(b-a)= 0- 36/(-1+3)= -18 10x+2= -18 x=-2 c=-2