Let fx-x-x-x- R- Then f- 13-

Given: f(x)=x [x],x∈ R We know that, For 0≤ x lt;1,[x]=0. ∴ f(x)=x 0 ⇒ f(x)=x The differentiation of the given function for x∈ [0,1) f'(x)=d/dx(x) ⇒ f ...

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Standard XII

Mathematics

Second Derivative Test Failure Condition

Let fx=x-[x],...

Question

$L e t f (x) = x - [x], x \in R$ . $T h e n f^{'} (\frac{1}{3}) = . . .$

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Solution

Given:
$f (x) = x - [x], x \in R$

We know that, $F o r 0 \leq x < 1, [x] = 0.$

$∴ f (x) = x - 0$

$\Rightarrow f (x) = x$

The differentiation of the given function for

$x \in [0, 1)$

$f^{'} (x) = \frac{d}{d x} (x)$

$\Rightarrow f^{'} (x) = 1$

$∴ f^{'} (\frac{1}{3}) = 1$

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Second Derivative Test Failure Condition

Standard XII Mathematics

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Letf(x)=x−[x],x∈R. Thenf′(13)=...

Given: f(x)=x−[x],x∈R We know that, For0≤x<1,[x]=0. ∴f(x)=x−0 ⇒f(x)=x The differentiation of the given function for x∈[0,1) f′(x)=ddx(x) ⇒f′(x)=1 ∴f′(13)=1

$L e t f (x) = x - [x], x \in R$ . $T h e n f^{'} (\frac{1}{3}) = . . .$

Given:
$f (x) = x - [x], x \in R$

We know that, $F o r 0 \leq x < 1, [x] = 0.$

$∴ f (x) = x - 0$

$\Rightarrow f (x) = x$

The differentiation of the given function for

$x \in [0, 1)$

$f^{'} (x) = \frac{d}{d x} (x)$

$\Rightarrow f^{'} (x) = 1$

$∴ f^{'} (\frac{1}{3}) = 1$