The total cost function is given by $c(x) = \frac{1}{3}x^3 - 5x^2 + 30x - 15$ and selling price per unit is Rs.6. The profit is maximum if the value of x is:

The number of points of the local maximum value of the function $f(x) = 3x^4 + 4x^3 - 12x^2 + 2$ is,

If $f(x) = \sin x - \cos x$, $x \in [0, 2\pi]$ then

(A) $f(x)$ is increasing in $(0, \frac{3\pi}{4})$

(B) $f(x)$ is decreasing in $(0, \frac{3\pi}{4})$

(C) $f(x)$ is decreasing in $(\frac{3\pi}{4}, \frac{7\pi}{4})$

(D) $f(x)$ is decreasing in $(\frac{7\pi}{4}, 2\pi)$

Choose the correct answer from the options given below:

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:

Match List-I with List-II

Choose the correct answer from the options given below:

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

In which of the following interval, the function $f(x) = \frac{x}{\log x}$ is decreasing?