The length of a rectangle is decreasing at 4 cm/minute and the width is increasing at 3 cm/minute. The rate of change of area when length is 10cm and width is 6cm, is:

If $f(x) = (x+3)e^{-x}$, then which of the following statements are True?

(A) Function $f(x)$ is increasing on $(-2, \infty)$.

(B) Function $f(x)$ is decreasing on $(-2, \infty)$.

(C) Function $f(x)$ is increasing on $(-\infty, -2)$.

(D) Function $f(x)$ is decreasing on $(2, 3)$.

The points on the ellipse $4x^2 + y^2 = 4$ that are farthest from the point (1,0) are;

The slope of the normal to the curve $y = 2x^2 - 4$ at P (1, -2) is :

The sides of an equilateral triangle are increasing at the rate of 2 cm/sec. The rate at which the area increases when the side is 10 cm, is

The line $ax + by = 7$ is a tangent to the curve $y = \frac{x-7}{(x-2)(x-3)}$ at the point where it cuts the x-axis

A. The y-intercept of the line is $-0.7$

B. $b = -7$

C. $a = 1$

D. the line passes through the point $(-13, -1)$

E. $b = -20$

Choose the correct answer from the options given below:

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