हीरे को परखना है तो अँधेरे का इंतजार करो

धूप में तो काँच के टुकड़े भी चमकने लगते हैं||

**Topics discussed in this lecture:**

Uses and difference between a function and an equation

Difference between maxima / minima and maximum / minimum.

How to study NCERT exercise 6.5 maxima and minima

Different types of maxima / minima or maximum / minimum (Global maximum, global minimum, absolute maximum, absolute minimum, local maximum, local minimum)

NCERT EXERCISE 6.5 |

**Questions discussed in this lecture**

**Question 1. **Find the maximum and minimum values, if any, of the following functions given by

(i) f(x) = (2x – 1)^2 + 3

(ii) f(x) = 9x^2 + 12x + 2

(iii) f(x) = -(x – 1)^2 + 10

(iv) g(x) = x^3 + 1

**Question 2. **Find the maximum and minimum values, if any, of the following functions given by

(i) f(x) = |x + 2| – 1

(ii) g(x) = – |x + 1| + 3

(iii) h(x) = \sin (2x) + 5

(iv) f(x) = |\sin 4x + 3|

(v) h(x) = x + 1, x \in (-1, 1)