1. Tardigrade
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  4. The number of local extremum points of the function f(x)=e sin x+2 sin x+x-4 in (0, (π/2)) is [Note: [ k ] and operatornamesgn( k ) denotes greatest integer function and signum function of k respectively.]

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Q. The number of local extremum points of the function $f(x)=e^{\sin x}+2 \sin x+x-4$ in $\left(0, \frac{\pi}{2}\right)$ is
[Note: $[ k ]$ and $\operatorname{sgn}( k )$ denotes greatest integer function and signum function of k respectively.]

Application of Derivatives

Solution:

$f^{\prime}(x)=e^{\sin x} \cdot \cos x+2 \cos x+1>0$ for $x \in\left(0, \frac{\pi}{2}\right)$
No local extremum points of the function