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

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

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tangent of f(x)=((2x+1))/(x+2),\at x=1

tangent of

f (x) = \frac{( 2 x + 1 )}{x + 2}, at x = 1

y = \frac{1}{3} x + \frac{2}{3}

Solution steps

Find the tangent point:

(1, 1)

Find the slope of

f (x) = \frac{2 x + 1}{x + 2} : \frac{df ( x )}{d x} = \frac{3}{( x + 2 ) ^{2}}

Compute the slope of

f (x) = \frac{2 x + 1}{x + 2}

x = 1 : m = \frac{1}{3}

Find the line with slope m=

\frac{1}{3}

and passing through

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

y = \frac{1}{3} x + \frac{2}{3}

y = \frac{3 x - 4}{2 x + 3}

\frac{\partial}{\partial x} (x^{6} y^{6} + 9 x^{4} y)

\frac{d}{d x} ((4 x^{3} + 5 x^{2}) (9 x))

y = 2 x^{2} - 3 x, (2, 2)

x \to 2 - lim (\frac{x + 2}{x - 2})

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