What is the tangent of f(x)= 5/x ,\at x=9 ?

The tangent of f(x)= 5/x ,\at x=9 is y=-5/81 x+10/9

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tangent of f(x)= 5/x ,\at x=9

tangent of

f (x) = \frac{5}{x}, at x = 9

y = - \frac{5}{81} x + \frac{10}{9}

Solution steps

Find the tangent point:

(9, \frac{5}{9})

Find the slope of

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

Compute the slope of

f (x) = \frac{5}{x}

x = 9 : m = - \frac{5}{81}

Find the line with slope m=

- \frac{5}{81}

and passing through

(9, \frac{5}{9}) : y = - \frac{5}{81} x + \frac{10}{9}

y = - \frac{5}{81} x + \frac{10}{9}

\frac{d}{d x} (\frac{cos ( x )}{x ^{8}})

\frac{d}{d x} (\frac{1}{( 2 x + 3 ) ^{2}})

\int sin^{2} (x + 2) d x

\int 144 - t^{2} d t

What is the tangent of f(x)= 5/x ,\at x=9 ?
The tangent of f(x)= 5/x ,\at x=9 is y=-5/81 x+10/9