I: $f^{'} (a) = f^{''} (a) = f^{'''} (a) = 0$ and $f^{''''} (a) \neq 0$ then $f (x)$ attains maximum if $f^{''''} (a)$ is negative
II: Every maximum or minimum value must be at stationary value which of the above statements are true

only I

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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
Both the statements are true,which follows from standard results.

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Similar questions

Q. Match the following lists Let f(x) be any function

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 $x = a$

Q. Assertion (A): If f(x) = |x|, then f has minimum value at x = 0
Reason (R): A function f(x) has minimum value at x = a if

f^{'} (a) = 0

and

f^{''} (a) > 0

Q. I. lf

f^{'} (a) > 0

then

f

is increasing at

x = a

II: If f is increasing at

x = a

then

f^{'} (a)

need not to be positive

If $y = f (x),$ where $f : A \to B$ is a function in $x,$ then which of the following statements is true?

(i) Every element of $A$ needs to have an image.

(ii) $x \in A$ must be related to one and only one value of $y$ of $B .$

If y = f : A $\to$ B, then which of the following is true if f(x) is a function in x?

(i) x must be able to take each and every value of A.

(ii) one value of x must be related to one and only one value of y in set B.

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I: f′(a)=f′′(a)=f′′′(a)=0 and f′′′′(a)≠0 then f(x) attains maximum if f′′′′(a) is negativeII: Every maximum or minimum value must be at stationary value which of the above statements are true

The correct option is C both I and IIBoth the statements are true,which follows from standard results.

I: $f^{'} (a) = f^{''} (a) = f^{'''} (a) = 0$ and $f^{''''} (a) \neq 0$ then $f (x)$ attains maximum if $f^{''''} (a)$ is negative
II: Every maximum or minimum value must be at stationary value which of the above statements are true

The correct option is C both I and II
Both the statements are true,which follows from standard results.