Question

Find the points on the curve y=x+1/x at which tangent is parallel to the x axis

Answer 1

slope of the tangent to the curve is given by:-
dy/dx=1-1/x^2
since the tangent is parallel to x axis,dy/dx=0
=>1=1/x^2
=>x^2=1
=>x=+-1
and thus y=2 or -2
thus the points are:-(1,2) & (-1,-2)

Answer 2

The points on the curve y = x + 1/x at which tangent is parallel to the x axis are (1,2) & (-1,-2)

Given :

The curve y = x + 1/x

To find :

The points on the curve at which tangent is parallel to the x axis

Solution :

Step 1 of 3 :

Write down the given equation of the curve

The given equation of the curve is

$\displaystyle \sf{ y = x + \frac{1}{x} }$

Step 2 of 3 :

Find the slope of the curve

$\displaystyle \sf{ y = x + \frac{1}{x} }$

Differentiating both sides with respect to x we get

$\displaystyle \sf{ \frac{dy}{dx} = 1 - \frac{1}{ {x}^{2} } }$

So the slope of the curve is given by

$\displaystyle \sf{ \frac{dy}{dx} = 1 - \frac{1}{ {x}^{2} } }$

Step 3 of 3 :

Find the points

Since tangent is parallel to x axis

$\displaystyle \sf{ \frac{dy}{dx} = 0 }$

$\displaystyle \sf{ \implies 1 - \frac{1}{ {x}^{2} } = 0 }$

$\displaystyle \sf{ \implies {x}^{2} = 1}$

$\displaystyle \sf{ \implies x = \pm \: 1}$

For x = 1 we have y = 2

For x = - 1 we have y = - 2

Hence the required points are (1,2) & (-1,-2)

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