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  • Solve this problem - Limit , continuity and differentiability - JEE Main-20

f(x) = x^3 - 3x^2  has concaity upwards in the interval

  • Option 1)

    (1, \infty)

  • Option 2)

    (-\infty, \infty)

  • Option 3)

    (-1, \infty)

  • Option 4)

    (-\infty, 1)

 

Answers (1)

best_answer

As we have learned

Concavity, Convexity, of a function -

For concavity:

 If  f''(x)>0   in the interval   (a,b)  then shape of  f(x) in interval  (a,b)  is concave when observed from upwards or convex down.

For convexity:

If   f''(x)<0  in the interval  (a,b)  then it is convex upward or concave down.

- wherein

 

 f'(x) = 3x^{2}-6x\Rightarrow f''(x) =6x-6 = 6(x-1)

for concave up \rightarrow f''(x) > 0\Rightarrow 6(x-1)> 0\Rightarrow x> 1

 

 

 

 

 


Option 1)

(1, \infty)

Option 2)

(-\infty, \infty)

Option 3)

(-1, \infty)

Option 4)

(-\infty, 1)

Posted by

Himanshu

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