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  • Tell me? - Limit , continuity and differentiability - JEE Main-6

Total number of points of f(x) = x^3 - 3x^2 - 9x which one either local maxima or local minima is ?

  • Option 1)

    0

  • Option 2)

    1

  • Option 3)

    2

  • Option 4)

    3

 

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}-6x-9=3(x^{2}-2x-3)= 3(x-3)(x+1)

f'(x) will be zero at x= -1 and x= 3

\Rightarrow slope of tangent will be zero and also there will be sign change f"(x) at 3 and -1

 , so 2 points 

 

 


Option 1)

0

Option 2)

1

Option 3)

2

Option 4)

3

Posted by

Himanshu

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