Question

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

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

• A. A -4,B -2, C -3, D -5.
• B. A -2,B -4, C -3, D -1.
• C. A -2,B -4, C -3, D -5.
• D. A -2,B -4, C -5, D -1.

Answer 1

The correct option is B A -2,B -4, C -3, D -1.

If $f^{\prime }\left(a\right)=0$ and $f^{\prime \prime }\left(a\right)<0$, then there is a maximum at $x=a$

If $f^{\prime }\left(a\right)=0$ and $f^{\prime \prime }\left(a\right)>0$, then there is a minimum at $x=a$

If $f^{\prime }\left(a\right)\ne 0$ then $f\left(x\right)$ has neither minimum or maximum

If $f^{\prime }\left(a\right)>0$ then $f\left(x\right)$ is increasing at $x=a$