Since, f(x)=e-x (sinx-cosx) is a combination of exponential and trigonometric function which is continuous.
⇒ f(x)= e-x (sinx-cosx) is continuous on .
Here, f’(x)= e-x (sinx + cosx) - e-x (sinx – cosx)
= e-x cosx which exist in .
So, f(x)= e-x (sinx-cosx) is differentiable on
Conditions of Rolle’s theorem are satisfied.
Hence, there exist at least one such that f’(c)=0
i.e. e-c cos c =0
i.e. cos c = 0
Thus, Rolle’s theorem is satisfied.
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