Question

What is the maximum value of the function $f\left(x\right)=4{\sin }^{2}x+1?$

Answer 1

$f\left(x\right)=4{\sin }^{2}x+1$

For maximum value of $f\left(x\right),{\sin }^{2}x$ must be maximum, range of ${\sin }^{2}x$ is $[0,1]$.

1 is the maximum value of ${\sin }^{2}x$, let's put it in $f\left(x\right)$

$\Rightarrow f(x{)}_{max}=4(1)+1=5$