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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)
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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 })<f(x)  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)

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