Question

Verify the Lagrange’s Mean Value Theorem for the function f(x) given below and also
find c where f(x),(x-1),(x-2),(x-3) in (0,4)

Answer 1

Answer:

f(x)=(x−1)(x−2)(x−3)=(x

3

−6x

2

+11x−6)

f(x) is a cubic polynomial function and continuous at (0,4)

f'(x) =3x

2

−12x+11 exists

So f'(x) is differentiable at (0,4)

Now f'(c)=3c

2

−12c+11

Now f'(c)=

4−0

f(4)−f(0)

3c

2

−12c+11=

4

6−(−6)

=3

Solving we get c=2

−

+

3

2

=3.154 or 0.84

So c lies between (0,4)

Please mark it as brainliest answer