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

If the petrol burnt in driving a motor boat varies as the cube of the velocity,then the speed (in $km/h$) of the boat relative to the water,going against a water flow of $C \ km/h$,so that the quantity of petrol burnt is minimum,is:

Given $f(x) = e^{\sin x} + e^{\cos x}$. The global maximum value of $f(x)$

Let $f(x) = x^3 + px + 1$ and consider the following three statements:
$(i)$ For $p \geqslant 0$,$f(x) = 0$ has one negative root and $f(x)$ is monotonic.
$(ii)$ For $-1 < p < 0$,$f(x) = 0$ has one negative root and $f(x)$ is non-monotonic.
$(iii)$ For $p < -3/\sqrt[3]{4}$,$f(x) = 0$ has three real and distinct roots.
Which of the following is correct?

For the function $f(x) = \int_{0}^{x} \frac{\sin t}{t} dt$,where $x > 0$,which of the following is true?

Find the local minimum value of the function $f$ given by $f(x) = 3 + |x|, x \in R$.