The difference between the local extreme values of the function $f(x) = 2x^3 - 15x^2 + 36x + 40$ is ......

Prove that the function $f(x) = e^{x}$ does not have any maxima or minima.

If $y = \alpha \log x + \beta x^3 - x$ has extreme values at $x = -1$ and $x = 1$,then $\alpha$ and $\beta$ are respectively

Divide $10$ into two parts such that the sum of double of the first and the square of the second is minimum.

The cost function at American Gadget is $C(x) = x^3 - 6x^2 + 15x$ (where $x$ is in thousands of units and $x > 0$). The production level at which the average cost is minimum is:

The number of points of local maxima and local minima of the function $f(x) = |x^2 - 2|x||$ in $\mathbb{R}$ are $M$ and $m$ respectively. Then,the value of $2M + m$ is -