What is the tangent of f(x)=x+2/x ,(2,3) ?

The tangent of f(x)=x+2/x ,(2,3) is y= 1/2 x+2

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tangent of f(x)=x+2/x ,(2,3)

tangent of

f (x) = x + \frac{2}{x}, (2, 3)

y = \frac{1}{2} x + 2

Solution steps

Find the slope of

f (x) = x + \frac{2}{x} : \frac{df ( x )}{d x} = 1 - \frac{2}{x ^{2}}

Compute the slope of

f (x) = x + \frac{2}{x}

(2, 3) : m = \frac{1}{2}

Find the line with slope m=

\frac{1}{2}

and passing through

(2, 3) : y = \frac{1}{2} x + 2

y = \frac{1}{2} x + 2

\frac{1}{( 1 + x ^{2} ) ^{2}}

\frac{x + 1}{x + 7}

(2 x y^{2} + 2 y) + (2 x^{2} y + 2 x) y^{^{'}} = 0

e^{3 x} cos (6 x)

5 x y^{^{'}} - 2 y = 9 x^{2}

What is the tangent of f(x)=x+2/x ,(2,3) ?
The tangent of f(x)=x+2/x ,(2,3) is y= 1/2 x+2