For the function f(x)= sin x+3 x-2/(π)(x^2+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,

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

For the function f(x)= sin x+3 x-2/(π)(x^2+x), where x ∈[0, (π)/2], consider the…

Mathematics · 2024

JEE Main · 5 April 2024, Shift 1 · Q5

For the function

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

$$consider the following two statements :

(I)

$\displaystyle f$ is increasing in $\displaystyle \left(0, \frac{\pi}{2}\right)$.

(II)

$\displaystyle f^{\prime}$ is decreasing in $\displaystyle \left(0, \frac{\pi}{2}\right)$.

Between the above two statements,