What is the tangent of f(x)=(x-6)/(9x-1),\at x=1 ?

The tangent of f(x)=(x-6)/(9x-1),\at x=1 is y= 53/64 x-93/64

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tangent of f(x)=(x-6)/(9x-1),\at x=1

tangent of

f (x) = \frac{x - 6}{9 x - 1}, at x = 1

y = \frac{53}{64} x - \frac{93}{64}

Solution steps

Find the tangent point:

(1, - \frac{5}{8})

Find the slope of

f (x) = \frac{x - 6}{9 x - 1} : \frac{df ( x )}{d x} = \frac{53}{( 9 x - 1 ) ^{2}}

Compute the slope of

f (x) = \frac{x - 6}{9 x - 1}

x = 1 : m = \frac{53}{64}

Find the line with slope m=

\frac{53}{64}

and passing through

(1, - \frac{5}{8}) : y = \frac{53}{64} x - \frac{93}{64}

y = \frac{53}{64} x - \frac{93}{64}

m y d x = n x d y

\int_{0}^{1} \frac{1}{4 + x ^{2}} d x

x \to 0 lim ((\frac{1}{x} + 1)^{x})

p (x) = 0.7 x + 20, p (x) = \frac{547.8}{x + 15}

What is the tangent of f(x)=(x-6)/(9x-1),\at x=1 ?
The tangent of f(x)=(x-6)/(9x-1),\at x=1 is y= 53/64 x-93/64