What is the tangent of f(x)= x/(8-x),\at x=3 ?

The tangent of f(x)= x/(8-x),\at x=3 is y= 8/25 x-9/25

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tangent of f(x)= x/(8-x),\at x=3

tangent of

f (x) = \frac{x}{8 - x}, at x = 3

y = \frac{8}{25} x - \frac{9}{25}

Solution steps

Find the tangent point:

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

Find the slope of

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

Compute the slope of

f (x) = \frac{x}{8 - x}

x = 3 : m = \frac{8}{25}

Find the line with slope m=

\frac{8}{25}

and passing through

(3, \frac{3}{5}) : y = \frac{8}{25} x - \frac{9}{25}

y = \frac{8}{25} x - \frac{9}{25}

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

\int \frac{1}{( 6 + x ) ^{3}} d x

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

f (x) = \frac{sin ( x )}{2 x}

What is the tangent of f(x)= x/(8-x),\at x=3 ?
The tangent of f(x)= x/(8-x),\at x=3 is y= 8/25 x-9/25