Maxima and Minima

In a firm the cost function for output x is given as C = `"x"^3/3 - 20"x"^2 + 70 "x"`.  Find the 3 output for which marginal cost  (C_m) is minimum.

The total revenue function for a commodity is R `= 15x + x^2/3 - 1/36 x^4`. Show that at the highest point average revenue is equal to the marginal revenue.

Find the value of x for which the function `f(x) = x^3 - 3x^2 - 9x + 25` is increasing.

If f(x, y) is a homogeneous function of degree n, then `x (del "f")/(del x) + "y" (del "f")/(del y)` is equal to:

The average cost function associated with producing and marketing x units of an item is given by AC = 2x – 11 + `50/x`. Find the range of values of the output x, for which AC is increasing.

The maximum value of f(x) = sin x is:

A manufacturer can sell x items at a price of ₹ (280 - x) each .The cost of producing items is ₹ (x² + 40x + 35) Find the number of items to be sold so that the manufacturer can make maximum profit.

Find the local minimum and local maximum of y = 2x³ – 3x² – 36x + 10.