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

The tangent of f(x)=(2x)/(x+2),\at x=2 is y= 1/4 x+1/2

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tangent of f(x)=(2x)/(x+2),\at x=2

tangent of

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

y = \frac{1}{4} x + \frac{1}{2}

Solution steps

Find the tangent point:

(2, 1)

Find the slope of

f (x) = \frac{2 x}{x + 2} : \frac{df ( x )}{d x} = \frac{4}{( x + 2 ) ^{2}}

Compute the slope of

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

x = 2 : m = \frac{1}{4}

Find the line with slope m=

\frac{1}{4}

and passing through

(2, 1) : y = \frac{1}{4} x + \frac{1}{2}

y = \frac{1}{4} x + \frac{1}{2}

x y y^{^{'}} = 1 - x^{2}

\int \frac{1}{( x ^{2} - 64 ) ^{\frac{3}{2}}} d x

x \to 5 lim (c x^{2} + 6 x)

y = \frac{1}{2 x}

\int e^{\frac{x}{3} + 9} d x

What is the tangent of f(x)=(2x)/(x+2),\at x=2 ?
The tangent of f(x)=(2x)/(x+2),\at x=2 is y= 1/4 x+1/2