Application of Derivatives formulas, concepts, examples and worksheets
Download free study notes formulas, concepts, examples and worksheets of Application of Derivatives (CALCULUS)
Topics covered in AOD Module
Rate of change, Tangent and Normal, Error and Approximation, Rolle’s Theorem, LMVT, Monotonicity, Maxima & Minima.
Derivative as rate of change
In various fields of applied mathematics one has the quest to know the rate at which one variable is changing, with respect to other. The rate of change naturally refers to time. But we can have rate of change with respect to other variables also.
An economist may want to study how the investment changes with respect to variations in interest rates.
A physician may want to know, how small changes in dosage can affect the body’s response to a drug.
A physicist may want to know the rate of charge of distance with respect to time.
Definition : The average rate of change of a function f(x) with respect to x over an interval [a, a + h] is defined as 1/h[ f(a+h) – f(a) ]
Definition : The instantaneous rate of change of f(x) with respect to x is defined as f'(x) = lim h->0 1/h[ f(a+h) – f(a) ]
provided the limit exists.
Note : To use the word ‘instantaneous’, x may not be representing time. We usually use the word ‘rate of change’ to mean ‘instantaneous rate of change’.