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

The tangent of f(x)=((2x-1))/(x+3),\at x=2 is y= 7/25 x+1/25

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

tangent of

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

y = \frac{7}{25} x + \frac{1}{25}

Solution steps

Find the tangent point:

(2, \frac{3}{5})

Find the slope of

f (x) = \frac{2 x - 1}{x + 3} : \frac{df ( x )}{d x} = \frac{7}{( x + 3 ) ^{2}}

Compute the slope of

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

x = 2 : m = \frac{7}{25}

Find the line with slope m=

\frac{7}{25}

and passing through

(2, \frac{3}{5}) : y = \frac{7}{25} x + \frac{1}{25}

y = \frac{7}{25} x + \frac{1}{25}

f (x) = (2 x - 4)^{4} (x^{2} + x + 1)^{5}

\frac{\partial}{\partial x} (\frac{y}{2 - x})

f (x) = \frac{4 x - 1}{x + 5}

f (x) = (5 x - x^{2}) (5 - x - x^{2})

What is the tangent of f(x)=((2x-1))/(x+3),\at x=2 ?
The tangent of f(x)=((2x-1))/(x+3),\at x=2 is y= 7/25 x+1/25