Let $M$ and $m$ be respectively the local maximum and the local minimum values of the function $f(x) = 2x^3 - 9x^2 + 12x + 5$ in the interval $[0, 3]$. Then $M - m$ is equal to

Find all the points of local maxima and local minima of the function $f$ given by $f(x) = 2x^3 - 6x^2 + 6x + 5$.

For a steamer,the consumption of petrol (per hour) varies as the cube of its speed (in $km/hr$). If the speed of the current is steady at $C \, km/hr$,then the most economical speed of the steamer going against the current will be ........... $C$.

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

$A$ rectangle with its sides parallel to the $X$-axis and $Y$-axis is inscribed in the region bounded by the curves $y=x^2-4$ and $y=\frac{4-x^2}{2}$. The maximum possible area of such a rectangle is closest to the integer.

The figure shown below is the graph of the derivative of some function $y=f(x)$. Then,