For the function f(x)= sin x+3 x-2/(π)(x²+x), where x [0, (π)/2], consider the following two statements: (I) f is increasing in (0, (π)/2). (II) f^() is decreasing in (0, (π)/2). Between the above two statements,

(B) both (I) and (II) are true.

(D) neither (I) nor (II) is true.

Limit, Continuity and Differentiability: JEE Main 2024 Mathematics question

JEE Main 2024 · 5 Apr, Morning shift · Q2736

JEE Main 20245 Apr, Morning shiftMathematicsMediumLimit, Continuity and Differentiability420× since 2002

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,