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, 16:00: PM
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](https://images.topperlearning.com/topper/tinymce/cache/aaca970355036811af8ec25a833806b0.png)
Clearly, ![limit as straight x rightwards arrow 2 of straight f apostrophe left parenthesis straight x right parenthesis equals infinity](https://images.topperlearning.com/topper/tinymce/cache/bfdaac0acc03faa1cc3f41d38bdccae0.png)
![limit as straight x rightwards arrow 2 of straight f apostrophe left parenthesis straight x right parenthesis equals infinity](https://images.topperlearning.com/topper/tinymce/cache/bfdaac0acc03faa1cc3f41d38bdccae0.png)
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, 18:00: PM
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