Ask a Doubt
Request a call back

Join NOW to get access to exclusive study material for best results

CBSE Class 12-science Answered

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 | 04 Aug, 2014, 04:00: PM
answered-by-expert 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 | 04 Aug, 2014, 06:00: PM

Concept Videos

Multiple Choice Questions Practice Test Subjective Questions Webinar Subjective Questions Pre Board Assessment
Answered Unanswered My Questions My Answers
CBSE 12-science - Maths
Discuss the applicability of Rolle’s theorem for the following function on the indicated interval: f(x) = |x| on [–1, 1]
Asked by Topperlearning User | 04 Aug, 2014, 03:57: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 12-science - Maths
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 | 04 Aug, 2014, 04:00: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 12-science - Maths
Discuss the applicability of Rolle’s theorem for the following function on the indicated interval: f (x) = tan x on  [0, p]
Asked by Topperlearning User | 04 Aug, 2014, 04:03: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 12-science - Maths
Discuss the applicability of Rolle’s theorem on the function f (x) = open curly brackets table attributes columnalign left columnspacing 1.4ex end attributes row cell straight x plus 1 comma end cell cell when space 0 less or equal than straight x less or equal than 1 end cell row cell 3 minus straight x comma end cell cell when space 1 less or equal than straight x less or equal than 2 end cell end table close
Asked by Topperlearning User | 04 Aug, 2014, 04:11: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 12-science - Maths
Verify Rolle’s theorem for the function f (x) = x2 – 5x + 6 on the interval [2, 3].
Asked by Topperlearning User | 04 Jun, 2014, 01:23: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 12-science - Maths
Verify Rolle’s theorem for the function f (x) = (x – a)m (x – b)n on the interval [a, b], where m, n are positive integers.
Asked by Topperlearning User | 05 Aug, 2014, 08:38: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 12-science - Maths
Verify Rolle’s theorem for the function f (x) = square root of 4 minus straight x squared end root on [– 2, 2].
Asked by Topperlearning User | 04 Aug, 2014, 03:32: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 12-science - Maths
Verify Rolle's theorem for the function f (x) = log space open curly brackets fraction numerator straight x squared plus ab over denominator straight a left parenthesis straight a plus straight b right parenthesis end fraction close curly brackets on [a, b], where 0 < a < b.
Asked by Topperlearning User | 04 Aug, 2014, 03:48: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 12-science - Maths
Verify Rolle’s theorem for each of the following functions on indicated intervals : f(x) = sin x + cos x – on open square brackets 0 comma straight pi over 2 close square brackets
Asked by Topperlearning User | 04 Aug, 2014, 04:16: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 12-science - Maths
Verify Rolle's theorem for each of the following functions on indicated intervals : f (x) = sin x –  sin 2 x on [0, p]
Asked by Topperlearning User | 04 Aug, 2014, 04:35: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
My Class Videos Tests ₹ Plans Ask a Doubt