What is the tangent of f(x)=5-4/x ,(-1,1) ?

The tangent of f(x)=5-4/x ,(-1,1) is y=(12-8sqrt(2))x+13-8sqrt(2) \lor y=(12+8sqrt(2))x+13+8sqrt(2)

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tangent of f(x)=5-4/x ,(-1,1)

tangent of

f (x) = 5 - \frac{4}{x}, (- 1, 1)

y = (12 - 82) x + 13 - 82 or y = (12 + 82) x + 13 + 82

Solution steps

Slope of the tangent line at

(- 1, 1) : m = \frac{- 4 + 4 x}{x ( x + 1 )}

Find the slope of

f (x) = 5 - \frac{4}{x} : m = \frac{4}{x ^{2}}

Solve

\frac{4}{x ^{2}} = \frac{- 4 + 4 x}{x ( x + 1 )} : x = 1 + 2, x = 1 - 2

Find the tangent line at

x = 1 + 2 : y = (12 - 82) x + 13 - 82

Find the tangent line at

x = 1 - 2 : y = (12 + 82) x + 13 + 82

y = (12 - 82) x + 13 - 82 or y = (12 + 82) x + 13 + 82

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What is the tangent of f(x)=5-4/x ,(-1,1) ?
The tangent of f(x)=5-4/x ,(-1,1) is y=(12-8sqrt(2))x+13-8sqrt(2) \lor y=(12+8sqrt(2))x+13+8sqrt(2)