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  • Confused! kindly explain, - Limit , continuity and differentiability - JEE Main-14

Which of the following functions is decreasing on \mathbb R ?

  • Option 1)

    -x^2

  • Option 2)

    -x - x^3

  • Option 3)

    \sin x

  • Option 4)

    x^2 + x

 

Answers (1)

best_answer

As we have learned

Condition for Decreasing function -

The tangents drawn at any point on it make an obtuse angle with positive direction of  the x-axis.

M_{T}=tan\theta\leq 0

\therefore \:\:\frac{dy}{dx}\leq 0\:\:\:\:\:x\epsilon (a,b)

-

 

 (A) has derivative = -2x

 (B) has derivative = -1-3x^{2}

 (C) has derivative = \cos x

 (D) has derivative = 2x+1

out of these -2x, \cos x, 2x+1 changes sign while  -1-3x^{2} don't change sign and is only negative so decreasing 

 

 

 

 


Option 1)

-x^2

Option 2)

-x - x^3

Option 3)

\sin x

Option 4)

x^2 + x

Posted by

Himanshu

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