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  • Please,please help me - Limit , continuity and differentiability - JEE Main-12

Let f(x) = x^3 -9x then f(x) has 

  • Option 1)

    Local minima at x =-\sqrt(3)

  • Option 2)

    local minima at x = \sqrt(3)

  • Option 3)

    Local maxima at x = \sqrt(3)

  • Option 4)

    No local minima or maxima

 

Answers (1)

best_answer

As we have learned

Methods to find points of Local maxima and Local minima -

At points of local maxima and local minima the slope of tangent drawn to the curve is zero.For local maximum dy / dx changes from positive to negative and for local minimum dy / dx change negative to positive.

- wherein

 

 

f'(x)= 3x^{2}-9= 3(x^{2}-3)= 3(x+\sqrt3)(x-\sqrt3)

\Rightarrow f'(x) changes sign from negative to positive at x= +\sqrt3 and from positive to negative at x=- \sqrt3 so local minima at x= + \sqrt3 and local maxima at x = - \sqrt3

 

 

 

 

 


Option 1)

Local minima at x =-\sqrt(3)

Option 2)

local minima at x = \sqrt(3)

Option 3)

Local maxima at x = \sqrt(3)

Option 4)

No local minima or maxima

Posted by

Himanshu

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