Question

Find the intervals in which the function f(x) = log x/x is strictly increasing or strictly decreasing.

Find the absolute maximum and absolute minimum values of the function f given by f(x) = x/2 + 2/x, on the interval [1, 2].

The volume of a cube is increasing at the rate of 6 cm³/s. How fast is the surface area of cube increasing, when the length of an edge is 8 cm?

Given a curve y = 7x − x³ and x increases at the rate of 2 units per second. The rate at which the slope of the curve is changing, when x = 5 is :

A rectangular visiting card is to contain 24 sq.cm. of printed matter. The margins at the top and bottom of the card are to be 1 cm and the margins on the left and right are to be 1½ cm as shown below :