नज़र-नज़र में उतरना कमाल होता है,

नफ़स-नफ़स में बिखरना कमाल होता है,

बुलंदियों पे पहुँचना कोई कमाल नहीं,

बुलंदियों पे ठहरना कमाल होता है।

# Lecture - 2 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, questions based on this topic from NCERT Exercise 6.2

**Questions discussed in this lecture:**

NCERT EXERCISE 6.2 (Increasing and Decreasing Functions) |

**Question 1.** Show that the function given by f (x) = 3x + 17 is increasing on **R**.

**Question 2.** Show that the function given by f (x) = e^{2x} is increasing on **R**.

**Question 3.** Show that the function given by f (x) = sin x is

(a) increasing in \( \left( 0, \frac{\pi}{2} \right) \)

(b) decreasing in \( \left( \frac{\pi}{2}, \pi \right) \)

(a) neither increasing nor decreasing in \( (0, pi) \)

**Question 4.** Find the intervals in which the function *f* given by \( f(x) = 2x^2 + 3x \) is

(a) increasing

(b) decreasing

**Question 5.** Find the intervals in which the function *f* given by \( f(x) = 2x^3 – 3x^2 – 36x + 7 \) is

(a) increasing

(b) decreasing

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

(a) \( x^2 + 2x -5 \)

(b) \( 10 – 6x – 2x^2 \)

(c) \( -2x^3 – 9x^2 – 12x + 1 \)

(d) \( 6 – 9x – x^2 \)