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

The tangent of f(x)=(2x+5)/(5x-1),\at x=-1 is y=-3/4 x-5/4

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tangent of f(x)=(2x+5)/(5x-1),\at x=-1

tangent of

f (x) = \frac{2 x + 5}{5 x - 1}, at x = - 1

y = - \frac{3}{4} x - \frac{5}{4}

Solution steps

Find the tangent point:

(- 1, - \frac{1}{2})

Find the slope of

f (x) = \frac{2 x + 5}{5 x - 1} : \frac{df ( x )}{d x} = - \frac{27}{( 5 x - 1 ) ^{2}}

Compute the slope of

f (x) = \frac{2 x + 5}{5 x - 1}

x = - 1 : m = - \frac{3}{4}

Find the line with slope m=

- \frac{3}{4}

and passing through

(- 1, - \frac{1}{2}) : y = - \frac{3}{4} x - \frac{5}{4}

y = - \frac{3}{4} x - \frac{5}{4}

\int \frac{x ^{2} + 6 x}{x ^{3} - x ^{2} + x - 1} d x

x \to 2 lim ((x + 1) \cdot (x + 3))

\frac{\partial}{\partial x} (x e^{- x} (a + b x + c x^{2}))

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

x \to 2 lim (\frac{1}{x ^{2} - 4})

What is the tangent of f(x)=(2x+5)/(5x-1),\at x=-1 ?
The tangent of f(x)=(2x+5)/(5x-1),\at x=-1 is y=-3/4 x-5/4