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  • Give answer! - Limit , continuity and differentiability - JEE Main-9

Which of the following is increasing on \mathbb R ?

  • Option 1)

    x^2

  • Option 2)

    x^3 + x

  • Option 3)

    \sin x

  • Option 4)

    x^2 -x

 

Answers (1)

best_answer

As we have learned

Condition for increasing functions -

For increasing function tangents drawn at any point on it makes an acute slope with positive x-axis.

M_{T}=tan\theta\geq 0

\therefore \:\:\:\frac{dy}{dx}=f'(x)\geq 0\:\:for\:\:x\epsilon (a,b)

- wherein

Where f(x)  is continuous for (a,b)

 

x^{2} has derivative 2x  

\sin x has derivative cos x 

x^{2}-x has derivative 2x -1

All these derivatives changes sign on R

 But x^{3}+x has derivative 3x^{2}+1 which is only positive so x^{3}+x is increasing function  

 

 

 

 

 


Option 1)

x^2

Option 2)

x^3 + x

Option 3)

\sin x

Option 4)

x^2 -x

Posted by

Himanshu

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