If $f(x)$ is a function such that $f^{\prime}(x)=(x-1)^{2}(4-x),$ then

Let $k$ and $K$ be the minimum and the maximum values of the function $f(x) = \frac{(1 + x)^{0.6}}{1 + x^{0.6}}$ in $[0, 1]$ respectively,then the ordered pair $(k, K)$ is equal to

Find the absolute maximum and minimum values of a function $f$ given by $f(x) = 2x^{3} - 15x^{2} + 36x + 1$ on the interval $[1, 5]$.

If the sum of the lengths of the hypotenuse and a side of a right-angled triangle is given,show that the area of the triangle is maximum when the angle between them is $\frac{\pi}{3}$.

The perimeter of a sector is a constant. If its area is to be maximum,then the sectorial angle is

If $P(x) = a_0 + a_1x^2 + a_2x^4 + \dots + a_nx^{2n}$ is a polynomial in $x \in R$ with $0 < a_1 < a_2 < \dots < a_n$,then what does $P(x)$ have?