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  • Please help! - Limit , continuity and differentiability - JEE Main-16

Let f(x) = x^3 - x^2 then f(x) has 

  • Option 1)

    Local maxima at \frac{2}{}3

  • Option 2)

    Local maxima at 1

  • Option 3)

    Local minima at \frac{2}{}3

  • Option 4)

    No local maxima or minima

 

Answers (1)

best_answer

As we have learned

Method for maxima or minima -

First and second derivative method :

Step\:1.\:\:find\:values\:of\:x\:for\:\frac{dy}{dx}=0

Step\:2.\:\:x=x_{\circ }\:\:is\:a\:point\:of\:local\:maximum\:if\:f'(x)>0  and\:local\:minimum\:if\;f'(x)<0.

Step\:\:3.\:\:\:x=x_{\circ }\:\:is\:a\:point\:of\:local\:miximum\:if  f''(x)<0\:\:and\:local\:minimum\:if\:f''(x)>0

- wherein

Where\:\:y=f(x)

\frac{dy}{dx}=f'(x)

 

 f'(x) =3x^{2}-2x=0 \Rightarrow x= 0, 2/3

f''(x) =6x-2

f''(x) at x=0 is -2 so local maxima at x=0

f''(x) at x=2/3 is 2 so local minima at x= 2/3 

 

 

 

 

 


Option 1)

Local maxima at \frac{2}{}3

Option 2)

Local maxima at 1

Option 3)

Local minima at \frac{2}{}3

Option 4)

No local maxima or minima

Posted by

Himanshu

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