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Q.
Find the maximum value of $f(x) = sin(sinx)$ for all $x \in R$
Application of Derivatives
Solution:
We have $f(x) = sin\,(sin\,x)$, $x \in R$
Now, $-1 \le sin \,x \le 1$ for all $x \in R$
$\Rightarrow sin \left(-1\right) \le sin\left(sinx\right) \le sin \,1$ for all $x \in R$
[$\because sin\, x$ is an increasing function on $\left[-1,1 \right]$]
$\Rightarrow - sin\, 1 \le f\left(x\right) \le sin\, 1$ for all $x \in R$
This shows that the maximum value of $f\left(x\right)$ is $sin \,1$.