Application of DerivativeHard

Question

If f(x) = ,x ∈ , then

Options

A.f(x) has exactly one point of minima
B.f(x) has exactly one point of maxima
C.f(x) is increasing in
D.maxima occurs at x0 where x0 = cosx0

Solution

    
f′(x) =
The only factor in f¢(x) which changes sign is cosx - x.
Let us consider graph of y = cos x and y = x
It is clear from figure that for x ∈ (0, x0), cos x - x > 0 and for  x ∈
cos x - x < 0,    ⇒    f′(x) has maxima at x0

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