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

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

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

tangent of

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

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

Solution steps

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}

(1, 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}

\int (x \cdot (1 - x^{4})) d x

\frac{d y}{d x} = y^{2} x^{3}

\int \frac{2}{2 + e ^{x}} d x

x \to 3 lim (7 - 3 x)

\frac{\partial}{\partial x} (- 3 x^{2} - 4 x)

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