. Maxima and Minima We are using maxima and minima in our daily life as well as in every field such as chemistry, physics, engineering and in economics etc., In particular, we can use maxima and minima (i) To maximize the beneficial values like profit, efficiency, output of a company etc., - - (ii) To minimize the negative values like, expenses, efforts etc., (iii) Used in the study of inventory control, economic order quantity etc. . .
Increasing and decreasing functions Before learning the concept of maxima and minima, we will study the nature of the curve of a given function using derivative. (i) Increasing function A function f ( x ) is said to be increasing function in the interval [ a , b ] if f x f x < ⇒ ( ) ≤ ( ) for all x x a b ∈ A function f ( x ) is said to be strictly increasing in [ a , b ] if f x f x < ⇒ ( ) < ( ) for all x x a b ∈ Y y = f ( x ) f ( x ) f ( x ) x x f x f x < ⇒ < Strictly increasing function o Fig: . (ii) Decreasing function A function f ( x ) is said to be decreasing function in [ a , b ] if f x f x < ⇒ ( ) ≥ ( ) for all x x a b ∈ A function f ( x ) is said to be strictly decreasing function in [ a , b ] if f x f x < ⇒ ( ) > ( ) for all x x a b ∈ o Y f ( x ) f ( x ) x x f x f x < ⇒ > Strictly decreasing function Fig: . NOTE A function is said to be monotonic function if it is either an