The total revenue received from the sale of $x$ units of a product is given by $R(x)=24x+5x^2+3$. The marginal revenue when $x=10$ is,

The curve $x = y^2$ and $xy = k$ cut orthogonally, then $k^2$ is equal to:

The slope of normal to the curve $y = kx^2 - 3x + 2$ at $x = \frac{1}{2}$ is 5. The value of 'k' is

Which of the following functions are strictly decreasing on $\left(0, \dfrac{\pi}{2}\right)$?

A. $\cos x$

B. $-\cot x$

C. $\cos 2x$

D. $\sin x$

Choose the correct answer from the options given below:

If the interval in which the function $f(x) = 4x^3 - 6x^2 - 72x + 30$ is strictly decreasing, is (a,b) then a+b is equal to

The maximum value of f(x) = $\left(\frac{1}{x}\right)^x$ is

The edge of a cube is increasing at a rate of 7cm/s. The rate of change of area of the cube when edge of the cube is 3cm is: