Q. 25.0( 1 Vote )

# Verify Rolle’s th

Condition (1):

Since, f(x)=x2-x-12 is a polynomial and we know every polynomial function is continuous for all xϵR.

f(x)= x2-x-12 is continuous on [-3,4].

Condition (2):

Here, f’(x)=2x-1 which exist in [-3,4].

So, f(x)= x2-x-12 is differentiable on (-3,4).

Condition (3):

Here, f(-3)=(-3)2-3-12=0

And f(4)=42-4-12=0

i.e. f(-3)=f(4)

Conditions of Rolle’s theorem are satisfied.

Hence, there exist at least one cϵ(-3,4) such that f’(c)=0

i.e. 2c-1=0

i.e.

Value of

Thus, Rolle’s theorem is satisfied.

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