The maximum value of the function $f(x)=2x^3-15x^2+36x-48$ on the set $A=\{x \mid x^2+20 \leq 9x\}$ is

The function,$f(x)=x \sqrt{1-x}$,where $x \in(0,1)$,has a local maximum at $x=$

The adjacent sides of a rectangle with a given perimeter of $100 \, cm$ and enclosing the maximum area are:

The number of points of local maxima and local minima of the function $f(x) = |x^2 - 2|x||$ in $\mathbb{R}$ are $M$ and $m$ respectively. Then,the value of $2M + m$ is -

On the interval $[0,1]$,the function $f(x) = x^{25}(1-x)^{75}$ takes its maximum value at the point

The number of points at which the function $f(x) = \int\limits_0^x {{e^{t - 3}}} \left( {{t^2} + 2} \right)\left( {t - 3} \right){\left( {t + 4} \right)^2}dt$ has a local minimum is: