The cost function of a product is given by $C(x)=\frac{1}{3}x^3-45x^2-900x+36$, where x is the number of units produced. In order to minimize the marginal cost, how many units of the product must be produced?

The tangent to the curve $y = e^{3x}$ at the point $(0, 1)$, meets the x-axis at :

The number of tangents to the curve $xy - 3y + 2 = 0$ having slope 2 is:

The function $f(x) = 2x^3 - 3x^2 - 36x + 7$ is :

A. Increasing in $(-\infty,-2)$

B. Decreasing in $(-2,3)$

C. Neither increasing nor decreasing in $(-2,3)$

D. Increasing in $(3,\infty)$

Choose the correct answer from the options given below:

If the rate of change of area of a circle is equal to the rate of change of its diameter, then its radius is equal to :

The rate of change of the area of a circular disc with respect to its circumference when radius is 3 is :

The rate of change of $\sqrt{x^2-2}$ with respect to $\dfrac{x}{x+1}$ at $x=2$ is :