Mathematics Tes...

What will be the value of y''(x) for the given parametric form

 x = at, and  y = a/t

What is the maximum value of the functions \(f(x) = \frac{1}{\tan x+\cot x},\) where \(0 < x < \frac{\pi}{2}?\)

If 3^x + 3^y = 3^{x + y}, then find \(\rm dy\over dx\).

A balloon, which always remains spherical, has a variable diameter \(\rm{3\over2}(4x + 3)\). Find the rate of change of its volume with respect to x.

 Consider the following statements regarding the cost and revenue of a company. Which of the following statement is/are correct?

The velocity of telegraphic communication is given by \(v=x^2\log{\left(\frac{1}{x}\right) }\), where x is the displacement. For maximum velocity, x equal to

Let f(x) be a real -valued function such that f'(x₀) = 0 for some x₀ ∈ (0, 1), and f^"(x) > 0 for all x ∈ (0, 1). Then f(x) has

The price per unit of a commodity produced by a company is given by p = 30 - 2x and ‘x’ is the quantity demanded. What will be the marginal revenue when 5 commodities are in demand (or produced)?

A toy manufacturing firm assesses its variable cost to be ‘x’ times the sum of 30 and ‘x’, where ‘x’ is the number of toys produced, and also the cost incurred on storage is Rs. 1500. Find the marginal cost in Rs, when 20 toys are produced.

The range of values of k for which the function f(x) = (k² - 4)x² + 6x³ + 8x⁴ has a local maxima at point x = 0 is