The length of a rectangle is decreasing at the rate of 4 cm/minute and the width is increasing at the rate of 3 cm/minute, then the rate of change of the perimeter is

If $f(x) = \frac{1}{1-x}$, then for $x > 1, f(x)$ is:

The function $f(x) = \frac{4x^2+1}{x}$ is decreasing in

(A). $\left(\frac{-1}{2}, \frac{1}{2}\right)$

(B). $\left(-\infty, \frac{-1}{2}\right)$

(C). $\left(0, \frac{1}{2}\right)$

(D). $\left(\frac{-1}{2}, 0\right)$

Choose the correct answer from the options given below:

The maximum value of $\left(\frac{1}{x}\right)^x$ for $x > 0$ is

The point on the curve $y^2 = 8x$ for which the abscissa and ordinate change at the same rate, is

Based on above information answer the following question :

$\frac{dA(x)}{dx} =$

The demand function for a certain product is represented by the equation: $p = 20 + 5x - 3x^2$, where $x$ is the number of units demanded and $p$ is the price per unit (in Rs.), then the marginal revenue when 2 units are sold is: