Application of Derivatives
 For a quantity y varying with another quantity x, satisfying the rule y = f(x), the rate of change of y with respect to x is given by
The rate of change of y with respect to x at the point x = x_{0} is given by .
 If the variables x and y are expressed in form of x = f(t) and y = g(t), then the rate of change of y with respect to x is given by
 A function f: (a, b) → R is said to be
 increasing on (a, b), if x_{1} < x_{2} in (a, b)
 decreasing on (a, b), if x_{1} < x_{2} in (a, b)
OR
If a function f is continuous on [a, b] and differentiable on (a, b), then

…
To view the complete topic, please