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Find C of Rolle’s theorem for f(x) = ex(sin x - cos x) in
  • a)
    0
  • b)
    3π/4
  • c)
    π
  • d)
    Does not exist
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
Find C of Rolle’s theorem for f(x) = ex(sin x - cos x) ina)0b)3&...
Given function f(x) = ex(sin x - cos x)
f(x) is continuous in 3π/4
f(x) is differentiable in 

 
f(a) = f(b)
According to Rolle’s theorem,
there exists at least one value C ∈ (a,b)
such that f’(c) = 0
f’(c) = 0
f’(x) = ex (sin x – cos x) + ex (cos x + sin x)
f’(c) = ec (sin c – cos c) + ec (cos c + sin c) = 0
⇒ 2 ec sin c = 0

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