The difference between the absolute maximum and absolute minimum values of the function $f(x)=2x^3-15x^2+36x-30$ on the interval $[-1, 4]$ is:

If the function $f(x)=2 x^3-9 a x^2+12 a^2 x+1$,where $a > 0$,attains its local maximum and local minimum values at $p$ and $q$ respectively,such that $p^2=q$,then $f(3)$ is equal to:

The maximum value of $xy$ subject to $x + y = 8$ is

Let $f(x) = \int\limits_0^x \frac{\cos t}{t} dt, x > 0$. Then $f(x)$ has:

If $m$ and $M$ respectively denote the minimum and maximum of $f(x)=(x-1)^2+3$ for $x \in [-3, 1]$, then the ordered pair $(m, M)$ is equal to

If the extreme value of the function $f(x) = \frac{4}{\sin x} + \frac{1}{1 - \sin x}$ in the interval $[0, \frac{\pi}{2}]$ is $m$ and it exists at $x = k$,then $\cos k =$