Mathematics · essential
Rate of change interpretation for JEE
Applications of derivatives: Rate of change of quantities, monotonic-Increasing and decreasing functions, Maxima and minima of functions of one variable
Formula
\[\text{Average rate of change on }[a,b]=\frac{f(b)-f(a)}{b-a},\qquad \text{Instantaneous rate of change at }x=a=f'(a)\]
Variables: \(f\) is a function of one variable.
Conditions: For instantaneous rate, derivative should exist at \(a\).
Physical interpretation and application problems.