How do you find the value of c that satisfy the equation:

f(b)- f(a)/b-a = f'(c)

in the conclusion of the mean value theorem for the function
f(x)= 4x^2 + 4x -3 on the interval [-1,0]?

The value of c = -0.5∈ (-1,0)

Step-by-step explanation:

Step(i):-

Given function f(x) = 4x² +4x -3 on the interval [-1 ,0]

Mean Value theorem

Let 'f' be continuous on [a ,b] and differentiable on (a ,b). The there exists a Point 'c' in (a ,b) such that

Step(ii):-

Given  f(x) = 4x² +4x -3 …(i)

Differentiating equation (i) with respective to 'x'

          f¹(x) = 4(2x) +4(1) = 8x+4

Step(iii):-

By using mean value theorem

8c+4 = -3-(-3)

8c+4 = 0

8c = -4

c ∈ (-1,0)

Conclusion:-

The value of c = -0.5∈ (-1,0)

step-by-step explanation: