Q. 18

# Verify Rolle’s th

Condition (1):

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 .

Condition (2):

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

Condition (3):

Here,

And

i.e.

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

i.e.

Value of

Thus, Rolle’s theorem is satisfied.

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