Find the intervals in which the function f given f (x) = 2x³ - 3x² - 36x + 7 is
(a) Increasing   (b) Decreasing

Solution:

Increasing functions are those functions that increase monotonically within a particular domain,

and decreasing functions are those which decrease monotonically within a particular domain.

The given function is

f (x) = 2x³ - 3x² - 36x + 7

If the derivative is greater than 0 then the function is an increasing function.

Hence,

On differentiating wrt x, we get

f' (x) = 6x² - 6x - 36

= 6 (x² - x - 6)

= 6 (x + 2) ( x - 3)

Therefore,

f' ( x) = 0

⇒ x = - 2, 3

In (- ∞, - 2) and (3, ∞),

f' ( x) > 0

In (- 2, 3),

If the derivative is lesser than 0 then the function is a decreasing function. 

f' (x) < 0

Hence, f is strictly increasing in (- ∞, - 2), (3, ∞) and strictly decreasing in (- 2, 3)

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NCERT Solutions Class 12 Maths - Chapter 6 Exercise 6.2 Question 5

Find the intervals in which the function f given f (x) = 2x³ - 3x² - 36x + 7 is (a) Strictly increasing (b) Strictly decreasing

Summary:

The intervals in which the function f given f (x) = 2x³ - 3x² - 36x + 7 is strictly increasing in (- ∞, - 2), (3, ∞) and strictly decreasing in (- 2, 3)