NCERT solution Class 12 application of derivatives

NCERT Solutions

Class 12 Maths

Application of Derivatives

NCERT Questions

Ex.6.1 Q.1
Ex.6.1 Q.2
Ex.6.1 Q.3
Ex.6.1 Q.4
Ex.6.1 Q.5
Ex.6.1 Q.6
Ex.6.1 Q.7
Ex.6.1 Q.8
Ex.6.1 Q.9
Ex.6.1 Q.10
Ex.6.1 Q.11
Ex.6.1 Q.12
Ex.6.1 Q.13
Ex.6.1 Q.14
Ex.6.1 Q.15
Ex.6.1 Q.16
Ex.6.1 Q.17
Ex.6.1 Q.18
Ex.6.2 Q.1
Ex.6.1 Q.2
Ex.6.2 Q.3
Ex.6.2 Q.4
Ex.6.2 Q.5
Ex.6.2 Q.6
Ex.6.2 Q.7
Ex.6.2 Q.8
Ex.6.2 Q.9
Ex.6.2 Q.10
Ex.6.2 Q.11
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Ex.6.2 Q.13
Ex.6.2 Q.14
Ex.6.2 Q.15
Ex.6.2 Q.16
Ex.6.2 Q.17
Ex.6.2 Q.18
Ex.6.2 Q.19
Ex.6.3 Q.1
Ex.6.3 Q.2
Ex.6.3 Q.3
Ex.6.3 Q.4
Ex.6.3 Q.5
Ex.6.3 Q.6
Ex.6.3 Q.7
Ex.6.3 Q.8
Ex.6.3 Q.9
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Ex.6.3 Q.11
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Ex.6.3 Q.13
Ex.6.3 Q.14
Ex.6.3 Q.15
Ex.6.3 Q.16
Ex.6.3 Q.17
Ex.6.3 Q.18
Ex.6.3 Q.19
Ex.6.3 Q.20
Ex.6.3 Q.21
Ex.6.3 Q.22
Ex.6.3 Q.23
Ex.6.3 Q.24
Ex.6.3 Q.25
Ex.6.3 Q.26
Ex.6.3 Q.27
Ex.6.4 Q.1
Ex.6.4 Q.2
Ex.6.4 Q.3
Ex.6.4 Q.4
Ex.6.4 Q.5
Ex.6.4 Q.6
Ex.6.4 Q.7
Ex.6.4 Q.8
Ex.6.4 Q.9
Ex.6.5 Q.1
Ex.6.5 Q.2
Ex.6.5 Q.3
Ex.6.5 Q.4
Ex.6.5 Q.5
Ex.6.5 Q.6
Ex.6.5 Q.7
Ex.6.5 Q.8
Ex.6.5 Q.9
Ex.6.5 Q.10
Ex.6.5 Q.11
Ex.6.5 Q.12
Ex.6.5 Q.13
Ex.6.5 Q.14
Ex.6.5 Q.15
Ex.6.5 Q.16
Ex.6.5 Q.17
Ex.6.5 Q.18
Ex.3.5 Q.19
Ex.6.5 Q.20
Ex.6.5 Q.21
Ex.6.5 Q.22
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Ex.6.5 Q.24
Ex.6.5 Q.25
Ex.6.5 Q.26
Ex.6.5 Q.27
Ex.6.5 Q.28
Ex.6.5 Q.29
Ex.Misc.Q.1
Ex.Misc.Q.2
Ex.Misc.Q.3
Ex.Misc.Q.4
Ex.Misc.Q.5
Ex.Misc.Q.6
Ex.Misc.Q.7
Ex.Misc.Q.8
Ex.Misc.Q.9
Ex.Misc.Q.10
Ex.Misc.Q.11
Ex.Misc.Q.12
Ex.Misc.Q.13
Ex.Misc.Q.14
Ex.Misc.Q.15
Ex.Misc.Q.16
Ex.Misc.Q.17
Ex.Misc.Q.18
Ex.Misc.Q.19
Ex.Misc.Q.20
Ex.Misc.Q.21
Ex.Misc.Q.22
Ex.Misc.Q.23
Ex.Misc.Q.24
Ex.2.2 Q.21

Ex.6.2 Q.8

Find the values of x for which y = [x(x + 2)]² is an increasing function.

We have, y = [x(x + 2)]²= [x² + 2x]²

Now, = y’ = y = 2(x² + 2x)(2x - 2) = 4x(x - 2)(x - 1)

= 0

⟹ 4x(x - 2)(x - 1) = 0

⟹ x = 0, 1, 2

The points x = 0, x = 1, and x = 2 divide the real line into four disjoint intervals i.e. (-∞, 0),(0, 1)

(1, 2) and (2, ∞).

In intervals (-∞, 0) and (1, 2), < 0

So, y is strictly decreasing in intervals (-∞, 0) and (1, 2).

However, in intervals (0, 1) and (2, ∞), > 0

So, y is strictly increasing in intervals (0, 1) and (2, ∞).

Hence, y is strictly increasing for 0 < x < 1 and x > 2

Video solution:

Application of Derivatives Class 12 Maths NCERT Chapter 6 NCERT Solutions

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NCERT solutions of Application of Derivatives Class 12 Maths - all questions of all exercises are solved. Q. No. 1, 2, 3, and so on. Complete explanation and detailed solution makes them the best videos for Class 12 Maths Application of Derivatives NCERT solutions.