Verify Lagrange’s mean-value theorem for the following function:

Given:

Since the f(x) is a polynomial function,

It is continuous as well as differentiable in the interval [-1,4].

=10

f' (c)=3c²+2c-6

⇒ 3 c²+2c-6=10

⇒ 3 c²+2c-16=0

⇒ 3 c²-6c+8c-16=0

⇒ 3c(c-2)+8(c-2)=0

⇒ (3c+8)(c-2)=0

2

Verify Lagrange’s mean-value theorem for the following function:

3

Verify Lagrange’s mean-value theorem for the following function:

5

Verify Lagrange’s mean-value theorem for the following function:

6

Verify Lagrange’s mean-value theorem for the following function: