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Find the intervals in which the function f given by f(x) = 2x2 − 3x is strictly increasing strictly decreasing

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Question

Find the intervals in which the function f given by f(x) = 2x2 − 3x is

  1. strictly increasing
  2. strictly decreasing
Sum
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Solution

f(x) = 2x2 - 3x

f'(x) = 4x - 3

If f'(x) = 0

4x - 3 = 0

x = `3/4`

(a) f'(x) = 4x - 3 > 0, x `in (3/4, infty)`

Therefore, the function is continuously increasing in `(3/4, infty)`.

(b) f'(x) = cos x < 0, x `in (- infty, 3/4)`

Therefore, the function is continuously decreasing in `(- infty, 3/4)`.

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Chapter 6: Application of Derivatives - Exercise 6.2 [Page 205]

APPEARS IN

NCERT Mathematics Part 1 and 2 [English] Class 12
Chapter 6 Application of Derivatives
Exercise 6.2 | Q 4 | Page 205

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