Discuss the applicability of Rolle’s theorem for the following function  on the indicated interval :
f (x) = 3 + (x – 2)2/3 on [1, 3]

Asked by Topperlearning User | 4th Aug, 2014, 04:00: PM

Expert Answer:

We have,

f (x) = 3 + (x – 2)2/3, x Î [1, 3]
Þ f ¢ (x) = open parentheses 2 over 3 close parentheses left parenthesis x minus 2 right parenthesis to the power of minus bevelled 1 third end exponent 
Clearly, limit as straight x rightwards arrow 2 of straight f apostrophe left parenthesis straight x right parenthesis equals infinity
So, f (x) is not differentiable at x = 2 Î (1, 3)
Hence, Rolle’s theorem is not applicable to f (x) = 3 + (x – 2)2/3 on the interval [1, 3]

Answered by  | 4th Aug, 2014, 06:00: PM