Introduction Differential Calculus Applications

In higher secondary first year we discussed the theoretical aspects of differential calculus, assimilated the process of various techniques involved and created many tools of differentiation. Geometrical and kinematical significances for first and second order derivatives were also interpreted. Now let us learn some practical aspects of differential calculus.
At this level we shall consider problems concerned with the applications to (i) plane geometry, (ii) theory of real functions, (iii) optimisation problems and approximation problems.

Derivative as a rate measure :
If a quantity y depends on and varies with a quantity x then the rate of change of y with respect to x is dy/dx .
Thus for example, the rate of change of pressure p with respect to height h is dp/dh . A rate of change with respect to time is usually called as ‘the rate of change’, the ‘with respect to time’ being assumed. Thus for example, a rate of change of current ‘i’ is di/dt and a rate of change of temperature ‘θ’ is dθ/dt and so on.