SATHEE: Application of Derivatives 4 Question 30

Application of Derivatives 4 Question 30

####32. The function $f (x) = 2 | x | + | x + 2 | - | | x + 2 | - 2 | x | |$ has a local minimum or a local maximum at $x$ is equal to

(2013 Adv.)

(a) -2

(b) $\frac{- 2}{3}$

(d) $2 / 3$

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Answer:

Correct Answer: 32. $(a, b)$

Solution:

PLAN

$\begin{aligned} We know that, | x | = \begin{array}{c} x, if x \geq 0 \\ - x, if x < 0 \end{array} \\ \Rightarrow | x - a | = \begin{array}{cc} x - a, & if x \geq a \\ - (x - a), & if x < a \end{array} \end{aligned}$

and for non-differentiable continuous function, the maximum or minimum can be checked with graph as

Here, $f (x) = 2 | x | + | x + 2 | - | | x + 2 | - 2 | x | |$ $- 2 x - (x + 2) + (x - 2)$ , if when $x \leq - 2$ $- 2 x + x + 2 + 3 x + 2,$ if when $- 2 < x \leq - 2 / 3$

$\begin{aligned} = - 4 x, if when - \frac{2}{3} < x \leq 0 \\ 4 x, if when 0 < x \leq 2 \\ 2 x + 4, if when x > 2 \\ - 2 x - 4, if x \leq - 2 \\ 2 x + 4, if - 2 < x \leq - 2 / 3 \\ = - 4 x, if - \frac{2}{3} < x \leq 0 \\ 4 x, if 0 < x \leq 2 \\ 2 x + 4, if x > 2 \end{aligned}$

Graph for $y = f (x)$ is shown as

Application of Derivatives 4 Question 30

Answer:

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Application of Derivatives 4 Question 30

Answer:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

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