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

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:

For the function $f(x) = e^{-2x}(2-x)^2$, the point of local maxima is:

The interval in which the function $f(x)=x^4-\dfrac{x^3}{3}$ is increasing, is

If the function $f(x) = 2x^3 + 9x^2 + 12x-1$ is given,then $f(x)$ have

The function $f(x) = 24x^4 - 32x^3 - 96x^2 + 7$ on the interval $\left[-\dfrac{3}{2}, 4\right]$ is :

A. increasing in $(-1,0)$

B. decreasing in $(0,4)$

C. increasing in $(2,4)$

D. decreasing in $\left(-\dfrac{3}{2},-1\right)$

Choose the correct answer from the options given below:

If the function $f(x)=\sin x+\cos x, 0 \le x \le 2\pi$ is increasing in the interval $(\alpha,\beta) \cup (\gamma,\delta)$, then $\alpha+\beta+\gamma+\delta$ is equal to: