The demand function for a certain product is represented by $p = 35 + 5x - 3x^2$, where $x$ is the number of units demanded and $p$ is the price per unit. The marginal revenue when 2 units are sold is

The interval in which the $f(x) = \sin x - \cos x$, $0 \leq x \leq 2\pi$ is strictly decreasing is :

If the total cost function is given by $C(x)=\frac{x^3}{3}-2x^2+9x-70$ and the selling price per unit is ₹6, then for what value of $x$ will the profit be maximum?

A solid sphere of gold of radius 5 cm, is being melted in a furnace such that the radius is decreasing uniformly. When the radius is 1cm, the rate at which surface area (A) is decreasing w.r.t. time ($t$) is equal to

($\frac{dv}{dt}$ = rate at which volume is decreasing w.r.t. $t$)

The demand for a certain product is represented by the function

$p = 150 + 10x - x^2$ (in Rs.)

where $x$ is the number of units demanded and $p$ is the price per unit, then the value of marginal revenue, when 10 units are sold is

The function $f(x) = x^3 + 2x^2 - 1$ is

(A) increasing in $\left(\dfrac{-4}{3}, 0\right)$

(B) decreasing in $\left(\dfrac{-4}{3}, 0\right)$

(C) increasing in $\left(-\infty, \dfrac{-4}{3}\right)$

(D) increasing in $(0, \infty)$

Choose the correct answer from the options given below:

A function $f(x)$ is defined as:

$f(x) = x^3-6x^2+9x+15$

For the function $f(x)$, which of the following statements are correct ?

(A) The critical points are $x=1$ and $x=3$.

(B) $x=1$ is a point of local minimum.

(C) The local maximum value is 19.

(D) $x=3$ is a point of local minimum.

Choose the correct answer from the options given below: