CUET Preparation Today
CUET
-- Mathematics - Section A
Applications of Derivatives
The maximum value of $(\sin x)^{(\sin x)}$ is:
7/3
7
π/2
1
$f(x)=(\sin x)^{\sin x}⇒f'(x)=(\sin x)^{\sin x}[\cos x+\cos x.\log(\sin x)]=0$
$⇒\cos x(1+\log(\sin x))=0$
$⇒x=π/2$
$f''(π/2)<0$ Maximum value = $f(π/2)=(1)^1=1$
