What is the tangent of f(x)= 9/(8-x) ?

The tangent of f(x)= 9/(8-x) is y= 9/((8-a_{0))^2}x+(-18a_{0}+72)/((-a_{0)+8)^2}

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tangent of f(x)= 9/(8-x)

tangent of

f (x) = \frac{9}{8 - x}

y = \frac{9}{( 8 - a _{0} ) ^{2}} x + \frac{- 18 a _{0} + 72}{( - a _{0} + 8 ) ^{2}}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, \frac{9}{8 - a _{0}})

Find the slope of

f (x) = \frac{9}{8 - x} : \frac{df ( x )}{d x} = \frac{9}{( 8 - x ) ^{2}}

EN : T i tl e G e n er a l Eq u a t i o n Sl o p e A t P o in t 2 Eq : m = \frac{9}{( 8 - a _{0} ) ^{2}}

Find the line with slope m=

\frac{9}{( 8 - a _{0} ) ^{2}}

and passing through

(a_{0}, \frac{9}{8 - a _{0}}) : y = \frac{9}{( 8 - a _{0} ) ^{2}} x + \frac{- 18 a _{0} + 72}{( - a _{0} + 8 ) ^{2}}

y = \frac{9}{( 8 - a _{0} ) ^{2}} x + \frac{- 18 a _{0} + 72}{( - a _{0} + 8 ) ^{2}}

What is the tangent of f(x)= 9/(8-x) ?
The tangent of f(x)= 9/(8-x) is y= 9/((8-a_{0))^2}x+(-18a_{0}+72)/((-a_{0)+8)^2}