The function $f(x) = x^2e^{-2x}$ increases on

Rate of change of area of a circle with respect to radius

(A) When r = 2 cm is $4\pi$ cm²/cm.

(B) When r = 6 cm is $12\pi$ cm²/cm.

(C) When r = 12 cm is $6\pi$ cm²/cm.

(D) When r = 16 cm is $8\pi$ cm²/cm.

Choose the correct answer from the options given below:

Angle between tangents to the curve $y = x^2 - 5x + 6$ at the points (2, 0) and (3, 0) is :

The sides of an equilateral triangle are increasing at the rate of 5 cm/sec. The rate at which the area increases when the side is 20 cm, is

The real valued function $f(x) = x^{15} + 5x^9 + 10$ is increasing for___________.

Based on above information answer the following question :

$x$ and $y$ will satisfy :

Let f be a function defined by $f(x) = 2x^3 - 3x^2 - 36x + 2$, then which of the following are correct?

(A) The critical points of f(x) are -2 and 3.

(B) The function f(x) increases in the interval $(3, \infty)$

(C) The function f(x) decreases in the interval (-2,3)

(D) The function f(x) increases in the interval (-2,3)

Choose the correct answer from the options given below: