The absolute maximum value of the function $f(x) = \frac{x}{2} + \frac{2}{x}$ in the interval $[-3, 3]$, is

The minimum value of $f(x) = |2x - 1|$ is

The function $f(x) = x^3 + 2x^2 - 1$ is

(A) increasing in $\left(\dfrac{-4}{3}, 0\right)$

(B) decreasing in $\left(\dfrac{-4}{3}, 0\right)$

(C) increasing in $\left(-\infty, \dfrac{-4}{3}\right)$

(D) increasing in $(0, \infty)$

Choose the correct answer from the options given below:

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 volume of a cube is increasing at the rate 9 $cm^3/s$. How fast is the surface area increasing when the length of an edge is 10 cm ?

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

(A). Increasing in the interval $\left(-\infty, -\frac{1}{2}\right)$

(B). Increasing in the interval $\left(-\frac{1}{2}, 0\right)$

(C). Decreasing in the interval $\left(0, \frac{1}{2}\right)$

(D). Decreasing in the interval $\left(\frac{1}{2}, \infty\right)$

Choose the correct answer from the options given below:

The equation of tangent to the curve given by $x = a\sin^3 t$, $y = b\cos^3 t$ at a point where $t = \frac{\pi}{2}$ is :