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

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

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tangent of f(x)=(4x)/(x+2),\at x=2

tangent of

f (x) = \frac{4 x}{x + 2}, at x = 2

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

Solution steps

Find the tangent point:

(2, 2)

Find the slope of

f (x) = \frac{4 x}{x + 2} : \frac{df ( x )}{d x} = \frac{8}{( x + 2 ) ^{2}}

Compute the slope of

f (x) = \frac{4 x}{x + 2}

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

Find the line with slope m=

\frac{1}{2}

and passing through

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

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

\frac{\partial}{\partial x} (\frac{y ^{2}}{x ^{2} + y ^{2}})

x^{3} - 11 x^{2} + 18 x, - x^{3} + 11 x^{2} - 18 x

\int \frac{- ln ( x )}{2} d x

f (x) = x^{2} 1 - x^{2}

f (x) = x^{3} - 3 x + 5

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