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

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

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

tangent of

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

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

Solution steps

Find the tangent point:

(2, \frac{5}{2})

Find the slope of

f (x) = \frac{5}{x} : \frac{df ( x )}{d x} = - \frac{5}{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{5}{4}

Find the line with slope m=

- \frac{5}{4}

and passing through

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

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

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x \to \infty lim (1 + x)

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