List of top Engineering Mathematics Questions on Functions

For the function \[ f(x) = x \sqrt{4 - x^2}, \] the maximum value in the range \(-2 \leq x \leq 2\) is ...................... (rounded off to two decimal places).

The function $f(x)=8\log_e x - x^2 + 3$ attains its minimum over the interval $[1,e]$ at $x=$ ____________.