Verify Rolle’s theorem for each of the following functions on indicated intervals :
f(x) = sin x + cos x – on 
Asked by Topperlearning User
| 4th Aug, 2014,
04:16: PM
Expert Answer:
Since sin x and cos x are everywhere continuous and differentiable. Therefore, f (x) = sin x + cos x – 1 is continuous on 
and differentiable on 
Also, f (0) = sin 0 + cos 0 – 1 = 0 and 
\ f (0) = 
Thus, f (x) satisfied conditions of Rolle’s theorem on Therefore, there exists c ε such that f ¢ (c) = 0
Therefore, there exists c ε such that f ¢ (c) = 0Þ cos x – sin x = 0 Þ sin x = cos x Þ tan x = 1 Þ x = 
Thus, c = 
such that f ¢ (c) = 0
such that f ¢ (c) = 0Hence, Rolle’s theorem is verified
Answered by
| 4th Aug, 2014,
06:16: PM
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