## Filters

Q&A - Ask Doubts and Get Answers
Q

# Help me understand! Which of the following graphs represents local minima at x = a ?

Which of the following graphs represents local minima at x = a ?

• Option 1)

• Option 2)

• Option 3)

• Option 4)

Answers (1)
145 Views

As we have learned

Local maximum and Local minimum -

Let  y = f(x)  be the given function then  $x=x_{\circ }$   is a point of local maximum if there exists an open interval containing  $x_{\circ }$  such that  $f(x_{\circ })>f(x)$

for all values of  x  lying in that interval and for $f(x_{\circ })  then it is local minimum in fig and at

$x=a,x=c\:\:\:Local\:\: maxima$

$and\:at\:\:x=b,x=d\:\:\:Local\:\: minima$

- wherein

Here (D) is the only case where we will have an interval in the neighbourhood of x= a which contains x=a and $f(a)< f(x)$

Option 1)

Option 2)

Option 3)

Option 4)

Exams
Articles
Questions