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 number of values of $x$ where the function $f(x) = \cos x + \cos (\sqrt{2} x)$ attains its maximum is

The two positive numbers with sum $t$,and the sum of their squares is minimum are

Let $f: R \to R$ be defined by $f(x) = \begin{cases} k - 2x, & \text{if } x \leqslant -1 \\ 2x + 3, & \text{if } x > -1 \end{cases}$. If $f$ has a local minimum at $x = -1$,then what is the possible value of $k$?

If the derivative of a function $f$ is given by $f'(x) = (x - a)^{2m} (x - b)^{2n + 1}$,where $m$ and $n$ are positive integers and $a > b$,then which of the following is true?

The lengths of the sides of a triangle are $10+x^2$,$10+x^2$ and $20-2x^2$. If for $x=k$,the area of the triangle is maximum,then $3k^2$ is equal to