How do you find the number c that satisfies the conclusion of the Mean Value Theorem for the function f(x) = x^2 + 4x + 2 on the interval [-3,-2]?

1 Answer
Oct 24, 2016

the value of c=-2.5

Explanation:

let c∈[-3,-2]

Then f'(c) can be calculated in 2 ways

The first way by differentiating f(x) as the function is continuous and differentiable on the interval [-3,-2]

f'(x)=2x+4 so f'(c)=2c+4

f(-3)=9-12+2=-1
f(-2)=4-8+2=-2
The second is from the definition of f'(c)

f'(c)=(f(-3)-f(-2))/(-3+2)=(-1+2)/(-1)=-1

therefore, 2c+4=-1 =>c=-2.5

and c∈[-3,-2]