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  • Help me solve this - Limit , continuity and differentiability - JEE Main-10

f(x) = x^4 + 2x^3 + 6x^2 + 12x has concavity  upwards only in the interval 

  • Option 1)

    (1, \infty)

  • Option 2)

    (-\infty,0)

  • Option 3)

    (0, \infty)

  • Option 4)

    (-\infty, \infty)

 

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) = 4x^{3}+6x^{2}+12x+12

f''(x) =12x^{2}+12x+12= 12(x^{2}+x+1)> 0\forall n\epsilon R

\because f''(x)> 0....\forall x\epsilon R
\Rightarrow f(x)  is concave up \forall n\epsilon R

 

 

 


Option 1)

(1, \infty)

Option 2)

(-\infty,0)

Option 3)

(0, \infty)

Option 4)

(-\infty, \infty)

Posted by

Himanshu

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