Question

f(x)=ex(sinx-cosx)or(π\4,5π\4)
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Answer 1

Answer:

Now, we have to show that, there exists a point c ∈ (π/4 , 5π/4) such that f'(c) = 0. ⇒ ec(sinc – cosc) + ec(cos c + sinc) = 0 ⇒ (sinc – cosc) + (cosc + sinc) = 0 ⇒ 2sinc = 0 ⇒ sinc = 0 ⇒ c = π ∈ (π/4 , 5π/4) Thus, all the conditions of Rolle’s theorem are verified.