If $A=\{x : 9x \geq x^2+20\}$ and $f: A \rightarrow R$ is defined by $f(x)=2x^3-15x^2+36x-48$,then the maximum value of $f(x)$ is

The values of $x$ at the stationary points of $f(x)=x^3+3x^2-2$ are

If $S_1$ and $S_2$ are respectively the sets of local minimum and local maximum points of the function $f(x) = 9x^4 + 12x^3 - 36x^2 + 25, x \in R$,then

Let a function $f(x)$ be defined as $f(x) = \begin{cases} \cos^{-1}(\mu) + x^2, & 0 < x < 1 \\ 4x, & x \geqslant 1 \end{cases}$. The function $f(x)$ can have a local minimum at $x = 1$ if the value of $\mu$ lies in the interval:

$A$ wire of length $28 \, m$ is to be cut into two pieces. One of the pieces is to be made into a square and the other into a circle. What should be the length of the two pieces so that the combined area of the square and the circle is minimum?

If $P(x) = a_0 + a_1x^2 + a_2x^4 + \dots + a_nx^{2n}$ is a polynomial in $x \in R$ with $0 < a_1 < a_2 < \dots < a_n$,then what does $P(x)$ have?