The total cost $c(x)$ associated with the production of $x$ units of an item is given by $c(x) = 0.001x^3 + 0.06x^2 + 20x + 500$. The marginal cost when 10 units are produced is:

The edge of a cube is increasing at a rate of 7 cm/s. The rate of change of area of the cube when its side is 3 cm is:

The rate of change of the area of a circle with respect to its radius $r$, when $r = 3$cm, is:

For the function $f(x) = (x+1)^2(x-2)^2$, which of the following statements are TRUE?

(A) $f(x)$ is decreasing on $(-\infty,-1)$

(B) $f(x)$ is increasing on $\left(-1,\frac{1}{2}\right)$

(C) $f(x)$ is decreasing on $\left(\frac{1}{2},2\right)$

(D) $f(x)$ is increasing on $(2,\infty)$

Choose the correct answer from the options given below:

The maximum area of a rectangle inscribed in a circle of radius $3\sqrt{2}$ cm, is:

If $y = ax^2 + bx$ has minima at $x = 2$ and the minimum value is -12, then which of the following are correct?

(A) $a = 3$

(B) $a = -3$

(C) $b = 12$

(D) $b = -12$

Choose the correct answer from the options given below:

The point of local maxima of the function $f(x) = (x - 2)^5(x + 2)^2$ is