Let f x -1- x 2 where the square root is to be taken positive- thenA- f has maxima at x -0B- f has no extrema at x-0C- f has minima at x -0D- f - exists at 0

The correct option is A f has maxima at x =0f(x) = 1 √(x^2) ⇒ f(x) = 1 |x| ∴ Max at x=0 and is 1 ...

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Standard XII

Mathematics

Global Maxima

Let f x =1-√ ...

Question

Let $f (x) = 1 - \sqrt{(x^{2})}$ where the square root is to be taken positive, then

f

has no extrema at

x = 0

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f

has minima at

x = 0

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f

has maxima at

x = 0

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f^{'}

exists at

0

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Solution

The correct option is C $f$ has maxima at $x = 0$
$f (x) = 1 - \sqrt{x^{2}} \Rightarrow f (x) = 1 - | x |$

$∴$ Max at $x = 0$ and is $1$

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Let f(x)=1−√(x2) where the square root is to be taken positive, then

The correct option is C f has maxima at x=0f(x)=1−√x2⇒f(x)=1−|x| ∴ Max at x=0 and is 1

Let $f (x) = 1 - \sqrt{(x^{2})}$ where the square root is to be taken positive, then

The correct option is C $f$ has maxima at $x = 0$
$f (x) = 1 - \sqrt{x^{2}} \Rightarrow f (x) = 1 - | x |$

$∴$ Max at $x = 0$ and is $1$