Lecture 3 Application of Derivatives

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).

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