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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 & 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) = e2x 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) $6 – 9x – x^2$

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