The total revenue received from the sale of $x$ units of a product is given by $R(x)=542+\dfrac{x^2+3}{4}$. What will be the marginal revenue when $x=24$ ?

The function $f(x)=\sin^4(x)+\cos^4(x)$, on interval $\left(0,\dfrac{\pi}{2}\right)$, has

If it is given that at $x = 1$, the function $f(x) = x^4 - 62x^2 + 2ax + b$ attains its maximum value on the interval [0, 2], then the value of a is:

The minimum value of $f(x) = e^x + e^{-x}$ is

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

Which of the following functions are increasing on $x \in \left(0, \frac{\pi}{2}\right)$?

(A) $f(x) = \sin x$

(B) $f(x) = \cos x$

(C) $f(x) = \tan x$

(D) $f(x) = \cos 3x$

Choose the correct answer from the options given below:

If $y = ax^2 + bx$ has minima at $x = 2$ and the minimum value is -12, then which of the following are correct?

(A) $a = 3$

(B) $a = -3$

(C) $b = 12$

(D) $b = -12$

Choose the correct answer from the options given below: