Request a call back

Verify Rolle’s theorem for the function f (x) = on [– 2, 2].
Asked by Topperlearning User | 04 Aug, 2014, 03:32: PM Expert Answer

Clearly, f (x) is defined for all x Î [– 2, 2] and has a unique value for each x Î [– 2, 2]. So, at each point of [–2, 2], the limit of f (x) is equal to the value of the function. Therefore, f (x) is continuous on [–2, 2].

Also, f ¢ (x) = exists for all x Î (–2, 2)
So, f (x) is differentiable on (–2, 2)
Also, f (–2) = f (2) = 0
Thus, all the three conditions of Rolle’s theorem are satisfied.
Now we have to show that there exists c Î (–2, 2) such that f ¢ (c) = 0
We have,
f (x) = Þ f ¢ (x) = \ f ¢ (x) = 0 Þ = 0 Þ x = 0
Since c = 0 Î (– 2, 2) such that f ¢ (c) = 0
Hence, Rolle’s theorem is verified.
Answered by | 04 Aug, 2014, 05:32: PM

## Concept Videos

CBSE 12-science - Maths
Asked by Topperlearning User | 04 Aug, 2014, 03:57: PM ANSWERED BY EXPERT
CBSE 12-science - Maths
Asked by Topperlearning User | 04 Aug, 2014, 04:00: PM ANSWERED BY EXPERT
CBSE 12-science - Maths
Asked by Topperlearning User | 04 Aug, 2014, 04:03: PM ANSWERED BY EXPERT
CBSE 12-science - Maths
Asked by Topperlearning User | 04 Aug, 2014, 04:11: PM ANSWERED BY EXPERT
CBSE 12-science - Maths
Asked by Topperlearning User | 04 Jun, 2014, 01:23: PM ANSWERED BY EXPERT
CBSE 12-science - Maths
Asked by Topperlearning User | 05 Aug, 2014, 08:38: AM ANSWERED BY EXPERT
CBSE 12-science - Maths
Asked by Topperlearning User | 04 Aug, 2014, 03:32: PM ANSWERED BY EXPERT
CBSE 12-science - Maths
Asked by Topperlearning User | 04 Aug, 2014, 03:48: PM ANSWERED BY EXPERT
CBSE 12-science - Maths
Asked by Topperlearning User | 04 Aug, 2014, 04:16: PM ANSWERED BY EXPERT
CBSE 12-science - Maths
Asked by Topperlearning User | 04 Aug, 2014, 04:35: PM ANSWERED BY EXPERT