Application of DerivativeHard
Question
For function f(x) = esinx - e-sinx, which of the following is/are correct -
Options
A.Equation of normal at x = π is x - 2y = π
B.f(x) is strictly increasing ∀ x ∈ 
; n ∈ I
; n ∈ IC.f(x) is strictly decreasing ∀ x ∈ 
; n ∈ I
; n ∈ ID.x = nπ, n∈I is either point of local maxima or minima of f(x).
Solution
y = f(x) = esinx - e-sinx
⇒ f′(x) = cosx(esinx + e-sinx)
f′(π) = - 2
⇒ slope of normal at x = π is
⇒ Equation of normal at x = π
⇒ x = 2y = π
sign of f′(x)
x = nπ is neither point of local maxima nor minima
⇒ f′(x) = cosx(esinx + e-sinx)
f′(π) = - 2
⇒ slope of normal at x = π is
⇒ Equation of normal at x = π
⇒ x = 2y = π
sign of f′(x)
x = nπ is neither point of local maxima nor minima
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