डर मुझे भी लगा फासला देख कर,

पर मैं बढ़ता गया रास्ता देख कर,

खुद ब खुद मेरे नज़दीक आती गई,

मेरी मंज़िल मेरा हौंसला देख कर।

# Lecture - 3 Chapter 6 Application of Derivatives

In this lecture, I am discussing how to find intervals in which the given function is increasing and decreasing. Also, more questions based on this topic from NCERT Exercise 6.2

**Questions discussed in this lecture:**

NCERT EXERCISE 6.2 (Increasing and Decreasing Functions) |

**Question 6.** Find the intervals in which the following functions are strictly increasing or decreasing:

(e) \( (x + 1)^3 (x – 3)^3 \)

**Question 7.** Show that \( y = \log_e(1 + x) – \frac{2x}{2 + x}, x>-1 \), is an increasing function of x throughout its domain.

**Question 8.** Find the values of x for which \( y = [x(x – 2)]^2 \) is an increasing function.

**Question 9.** Prove that \( y = \frac{4 \sin \theta}{(2 + \cos \theta)} – \theta \) is an increasing functions of \( \theta \) in \( \left[ 0, \frac{\pi}{2} \right] \)

**Question 10.** Prove that the logarithmic function is increasing on (0, ∞).

**Question 11.** Prove that the function f given by \( f(x) = x^2 – x + 1 \) is neither strictly increasing nor decreasing on (– 1, 1).