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  • Help me understand! - Limit , continuity and differentiability - JEE Main-11

Which of the following function is strictly increasing on \mathbb R ?

  • Option 1)

    x^3 + x^2 + x

  • Option 2)

    x + 2 \sin x

  • Option 3)

    \sin x

  • Option 4)

    x^ 2 +1

 

Answers (1)

best_answer

As we have learned

Strictly increasing functions -

A function f(x) is called strictly increasing in an interval l.

if\:for\:\:\:x_{1}<x_{2}\Rightarrow f(x_{1})<f(x_{2})
 

or\:if\:for\:\:\:x_{1}>x_{2}\Rightarrow f(x_{1})>f(x_{2})


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

 

- wherein

 

 x^{3}+x^{2}+x   has derivative 3x^{2}+2x+1  which has a> 0.. and .. D< 0 so 

3x^{2}+2x+1 is always positive , so x^{3}+x^{2}+x is strictly increasing

x+2\sin x  has derivative 1+2\cos x, which will change sign 

sin x has derivative cos x , which will change sign 

x^{2}+1  has derivative 2x, which will change sign 

 

 

 

 


Option 1)

x^3 + x^2 + x

Option 2)

x + 2 \sin x

Option 3)

\sin x

Option 4)

x^ 2 +1

Posted by

Himanshu

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