If f x is differentiable in the interval - 2-5 - where f 2 - 1 - 5 and f 5 - 1 - 2- then there exists a number c- 2 - c - 5 for which f- c -

The correct option is D 1 / 10 For nbsp; 2 lt;c lt;5 f'(c)=f(5) f(2)5 2 =0.5 0.23 =0.33 =0.1 =110 ...

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Standard XII

Mathematics

Integration by Substitution

If f x is d...

Question

If $f (x)$ is differentiable in the interval $[2, 5]$ , where $f (2) = \frac{1}{5}$ and $f (5) = \frac{1}{2}$ , then there exists a number $c$ , $2 < c < 5$ for which $f^{'} (c) =$

\frac{1}{2}

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\frac{1}{5}

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\frac{1}{10}

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None

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Solution

The correct option is D $\frac{1}{10}$
For
$2 < c < 5$
$f^{'} (c) = \frac{f (5) - f (2)}{5 - 2}$
$= \frac{0.5 - 0.2}{3}$
$= \frac{0.3}{3}$
$= 0.1$
$= \frac{1}{10}$

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Similar questions

If f (x) is differentiable in the interval [2, 5], where $f (2) = \frac{1}{5}$ and $f (5) = \frac{1}{2}$ , then there exists a number c, 2 < c < 5 for which f ' (c) is equal to

Q. If f(x) is differentiable in the interval [2, 5] and

f (2) = \frac{1}{5}; f (5) = \frac{1}{2}

. Then there exist a number ‘c’, 2 < c < 5 for which f’(c) is equal to

Q. Let

f (x)

is differentiable in

[2, 5]

. If

f (2) = \frac{1}{5}, f (5) = \frac{1}{2}

, then there exists a number

c, 2 < c < 5

for which

f^{'} (c)

is equal to

If f (x) is differentiable in the interval [2, 5], where $f (2) = \frac{1}{5}$ and $f (5) = \frac{1}{2}$ , then there exists a number c, 2 < c < 5 for which f ' (c) is equal to

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f (x) = | x - 2 | + | x - 5 |, x \in R

Statement 1:

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(2, 5)

and

f (2) = f (5)

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If f(x) is differentiable in the interval [2,5], where f(2)=15 and f(5)=12, then there exists a number c, 2<c<5 for which f′(c)=

The correct option is D 110For 2<c<5f′(c)=f(5)−f(2)5−2=0.5−0.23=0.33=0.1=110

If $f (x)$ is differentiable in the interval $[2, 5]$ , where $f (2) = \frac{1}{5}$ and $f (5) = \frac{1}{2}$ , then there exists a number $c$ , $2 < c < 5$ for which $f^{'} (c) =$

The correct option is D $\frac{1}{10}$
For
$2 < c < 5$
$f^{'} (c) = \frac{f (5) - f (2)}{5 - 2}$
$= \frac{0.5 - 0.2}{3}$
$= \frac{0.3}{3}$
$= 0.1$
$= \frac{1}{10}$