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Introduction

I: lf f'a<0...

Question

I: lf $f^{'} (a) < 0$ then the function $f$ is decreasing at $x = a$
II: lf $f$ is decreasing at $x = a$ then $f^{'} (a) < 0$
Which of the above statements are true ?

onlyI

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only II

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both I and II

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neither I nor II

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Solution

The correct option is C both I and II
(I) $f^{'} (a) < 0$ Which implies f is decreasing at $x = 0$
(II) If f is decresing at $x = a$
which implies $f^{'} (a) < 0$
has slope is negative for decreasing function

Suggest Corrections

Similar questions

f^{'} (a) > 0

f

x = a

x = a

f^{'} (a)

f^{'} (a) = 0

f^{''} (a) < 0

f (x)

x = a

List - I	List - II
A) $f^{'} (a) = 0$ and $f^{''} (a) < 0$ then	l) f(x) is increasing at $x = a$
B) $f^{'} (a) = 0$ and $f^{''} (a) > 0$ then	2) f(x) has maximum value at $x = a$
C) $f^{'} (a) \neq 0$ then	3) f(x) has neither maximum nor minimum
D) $f^{'} (a) > 0$	4) f(x) has minimum value at $x = a$
	5) f(x) is decreasing at $x = a$

f^{'} (a) = f^{''} (a) = f^{'''} (a) = 0

f^{''''} (a) \neq 0

f (x)

f^{''''} (a)

: f (x) = {log}_{a} x (x > 0)

a > 1

: f (x) = {log}_{a} x (x > 0)

0 < a < 1

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