The marginal cost (MC) and marginal revenue (MR) functions of a product are $MC = 20 + \frac{x}{20}$ and $MR = 30$ respectively. If the fixed cost is 200, then the maximum value of the profit is:

The function $f(x)=81-3x^3$ has

If a manufacturer's total cost 'C' is given by $C = \dfrac{x^2}{25} + 3x$, then the marginal cost when 7 units are produced will be:-

For the function $f(x) = e^{-2x}(2-x)^2$, the point of local maxima is:

Which of the following functions has a local minima at $x = 0$?

(A) $f(x) = x^3$

(B) $f(x) = |x|$

(C) $f(x) = x^2$

(D) $f(x) = x^{-2}$

Choose the correct answer from the options given below:

At x = 1, the function $f(x)=x^4-48x^2+\alpha x+120$ attains its maximum value in the interval [0, 2], then the value of $\alpha$ is:

Minimum value of D is :