The rate of change of volume of a sphere with respect to its surface area, when the radius is 6cm is:

The interval in which the function $f(x)=x^4-\dfrac{x^3}{3}$ is increasing, is

An open box is made from a cardboard measuring 12cm x 12cm by cutting off equal squares from the corner and turning up the side. Then maximum possible volume of the box would be:

The total cost $C(x)$ in Rupees associated with the production of $x$ units of an item is given by $C(x) = 0.007x^3 + 26x^2 + 15x + 400$. The marginal cost when 10 items are produced is:

The function $f:R\to R$ is defined by $f(x)=2x^3+5$, then which of the following statements are correct ?

(A) $f(x)$ has no local maximum value.

(B) $f(x)$ has no local minimum value.

(C) $f(x)$ has both local maximum and local minimum values.

(D) $f(x)$ has neither a local maximum value nor a local minimum value

Choose the correct answer from the options given below:

In a sphere of radius $r$, a right circular cone of height $h$ having a maximum curved surface area is inscribed. The expression for the curved surface area of the cone is

The interval in which the function $f(x) = x^2 - 3x + 7$ is increasing, is