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