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

If the local maximum value of the function $f(x)=x^3-2\lambda x^2+\lambda^2 x, \lambda>0$ is 108, Then the local minimum value of the function occurs at

The greatest possible value of '$a$' such that the function $f(x) = x^2 + a x + 1$ is always decreasing in the interval [1, 2] is:

Which of the following functions has a local minima at $x = 0$?

(A) $f(x) = x^3$

(B) $f(x) = |x|$

(C) $f(x) = x^2$

(D) $f(x) = x^{-2}$

Choose the correct answer from the options given below:

Which of the following statements are correct ?

A. The function $f(x) = a^x$ is increasing on $(-\infty,\infty)$ if $a>1$.

B. $f(x) = x^2 - 2x$ is decreasing in $(-\infty,1)$.

C. $f(x) = x(x-3)^2$ increases for $1 \le x \le 3$.

D. $f(x) = e^{-x}$ decreases in $[0,\infty)$.

Choose the correct answer from the options given below:

The appropriate change in the volume V of a cube of side $x$ metres caused by increasing the side by 2% is :

The point of local maxima of the function $f(x) = (x - 2)^5(x + 2)^2$ is