If f x = 2 sin ⁡ x - x 2 , then in x ∈ 0 , π

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Question: Answered & Verified by Expert

If

f (x) = 2 \sin x - x^{2}

, then in

x \in [0, π]

MathematicsApplication of DerivativesJEE Main

Options:

A $f (x)$ has no local maximum
B $f (x)$ has one local minimum
C $f (x)$ has $2$ local maxima
D $f (x)$ has one local maximum

Solution:

1143 Upvotes Verified Answer

The correct answer is:

f (x)

has one local maximum

f^{'} (x) = 2 (\cos x - x)

Thus,

x = α

is a local maxima for

f (x)

and no local minimum exists

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