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Application of Derivatives question

2024 · 5 Apr · Shift 1 · Q48

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JEE Main
Mathematics
Application of Derivatives
2024 · 5 Apr · Shift 1 · Q48

Application of Derivatives question

2024 · 5 Apr · Shift 1 · Q48

JEE MainMathematicsApplication of DerivativesMCQ+4 / −1

For the function

f(x)=\sin x+3 x-\frac{2}{\pi}\left(x^2+x\right), \text { where } x \in\left[0, \frac{\pi}{2}\right],

consider the following two statements : (I)

f

is increasing in

\left(0, \frac{\pi}{2}\right)

. (II)

f^{\prime}

is decreasing in

\left(0, \frac{\pi}{2}\right)

. Between the above two statements,

A
only (I) is true.
B
both (I) and (II) are true.
C
only (II) is true.
D
neither (I) nor (II) is true.

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