Problems on derivatives

Let me help you solving problems on derivatives. For instance, we will learn
how the derivative can be used (i) to determine rate of change of quantities, (ii) to find
the equations of tangent and normal to a curve at a point, (iii) to find turning points on
the graph of a function which in turn will help us to locate points at which largest or
smallest value (locally) of a function occurs.

Let me explain the sample problems on derivatives,
Example : Find the rate of change of the area of a circle per second with respect to
its radius r when r = 5 cm.

Solution : The area A of a circle with radius r is given by A = πr2. Therefore, the rate
of change of the area A with respect to its radius r is given by



When r = 5 cm, dA 10= π.
dr

Thus, the area of the circle is changing at the rate of
10π cm2/s.