What is the tangent of f(x)=(4x)/(x-3),\at x=5 ?

The tangent of f(x)=(4x)/(x-3),\at x=5 is y=-3x+25

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tangent of f(x)=(4x)/(x-3),\at x=5

tangent of

f (x) = \frac{4 x}{x - 3}, at x = 5

y = - 3 x + 25

Solution steps

Find the tangent point:

(5, 10)

Find the slope of

f (x) = \frac{4 x}{x - 3} : \frac{df ( x )}{d x} = - \frac{12}{( x - 3 ) ^{2}}

Compute the slope of

f (x) = \frac{4 x}{x - 3}

x = 5 : m = - 3

Find the line with slope m=

- 3

and passing through

(5, 10) : y = - 3 x + 25

y = - 3 x + 25

(\frac{10}{9}) t^{2}

5 y^{^{''}} + y^{^{'}} = - 6 x

\frac{\partial}{\partial x} (y - 3 x)

x \to 0 lim (\frac{x}{sin ( π x )})

x \to - \infty lim (x^{5})

What is the tangent of f(x)=(4x)/(x-3),\at x=5 ?
The tangent of f(x)=(4x)/(x-3),\at x=5 is y=-3x+25