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Standard XII

Mathematics

Angle between Two Lines

fc is a minim...

Question

$f (c)$ is a minimum value of $f (x)$ when at $x = c$

f^{'} (x)

changes sign form

+

ve to

-

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f^{'} (x)

changes sign from

-

ve to

+

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f^{'} (x)

does not change sign

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f^{'} (x)

is zero

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Solution

The correct option is B $f^{'} (x)$ changes sign from $-$ ve to $+$ ve
$f (c)$ is the minimum value of $y = f (x)$ if
$f^{'} (c) = 0$ and
$f^{''} (c) > 0$ .
That is slope of $y = f^{'} (x)$ changes from negative to positive at $x = c$ .

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f(c) is a minimum value of f(x) when at x=c

The correct option is B f′(x) changes sign from −ve to +vef(c) is the minimum value of y=f(x) if f′(c)=0 and f′′(c)>0.That is slope of y=f′(x) changes from negative to positive at x=c.

$f (c)$ is a minimum value of $f (x)$ when at $x = c$

The correct option is B $f^{'} (x)$ changes sign from $-$ ve to $+$ ve
$f (c)$ is the minimum value of $y = f (x)$ if
$f^{'} (c) = 0$ and
$f^{''} (c) > 0$ .
That is slope of $y = f^{'} (x)$ changes from negative to positive at $x = c$ .