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 = x₀ 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

1. A function f: (a, b) → R is said to be

• increasing on (a, b), if x₁ < x₂ in (a, b)
• decreasing on (a, b), if x₁ < x₂ in (a, b)

OR

If a function f is continuous on [a, b] and differentiable on (a, b), then

• f is increasing in [a, b], if for each xÎ (a, b)
• f is decreasing in[a, b], if for each xÎ (a, b)
• f is constant function in [a, b], if f…