If $y = \frac{\log x}{x^2}$, then $\frac{d^2y}{dx^2}$ is equal to

Any function f(x) is an increasing function in [a,b] if :

(A) $x_1, x_2 \in [a, b], f(x_1) \geq f(x_2)$ if $x_1 < x_2$

(B) $x_1, x_2 \in [a, b], f(x_1) \geq f(x_2)$ if $x_1 > x_2$

(C) (A) $x_1, x_2 \in [a, b], f(x_1) \leq f(x_2)$ if $x_1 < x_2$

(D) (A) $x_1, x_2 \in [a, b], f(x_1) < f(x_2)$ if $x_1 > x_2$

$\int \frac{dx}{x^{n+1} - x}\,dx$

Given that the total cost function for x units of a commodity is $C(x) = \dfrac{x^3}{4} + 4x^2 - 8x + 20$. Then the marginal cost when $x=4$ is:

If $f(x) = a\log|x| + \dfrac{b}{x} + x$ has its extreme values at $x = -1$ and $x = 3$, then $(a, b)$ is equal to:

Let $f : R \to R$ be a function defined as $f(x) = 2x^3 - 21x^2 + 36x - 20$, then :

(A) maximum value of $f(x)$ is $-3$

(B) minimum value of $f(x)$ is $-128$

(C) maximum value exists at $x = 6$

(D) minimum value exists at $x = 1$

Choose the correct answer from the options given below :

If the cost function and the profit function for a company is given by $C = 10 - 0.3x^2$ and $P = 0.3x^2 + 2x - 10$ respectively , where X represent units of output, then the revenue function is given by :