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

The tangent of f(x)=(1+2x)/(3+x),\at x=2 is y= 1/5 x+3/5

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

tangent of

f (x) = \frac{1 + 2 x}{3 + x}, at x = 2

y = \frac{1}{5} x + \frac{3}{5}

Solution steps

Find the tangent point:

(2, 1)

Find the slope of

f (x) = \frac{1 + 2 x}{3 + x} : \frac{df ( x )}{d x} = \frac{5}{( 3 + x ) ^{2}}

Compute the slope of

f (x) = \frac{1 + 2 x}{3 + x}

x = 2 : m = \frac{1}{5}

Find the line with slope m=

\frac{1}{5}

and passing through

(2, 1) : y = \frac{1}{5} x + \frac{3}{5}

y = \frac{1}{5} x + \frac{3}{5}

\frac{\partial}{\partial x} (5 2 x + 2 y)

\frac{d}{d x} y = (5 - x)^{63}

y = 3 x^{3} - x^{2} + 4, (2, 24)

h \to + 0 lim (\frac{8 ^{h} - 1}{h})

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

What is the tangent of f(x)=(1+2x)/(3+x),\at x=2 ?
The tangent of f(x)=(1+2x)/(3+x),\at x=2 is y= 1/5 x+3/5