What is the tangent of f(x)= 5/x ,\at x=4 ?

The tangent of f(x)= 5/x ,\at x=4 is y=-5/16 x+5/2

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tangent of f(x)= 5/x ,\at x=4

tangent of

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

y = - \frac{5}{16} x + \frac{5}{2}

Solution steps

Find the tangent point:

(4, \frac{5}{4})

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 = 4 : m = - \frac{5}{16}

Find the line with slope m=

- \frac{5}{16}

and passing through

(4, \frac{5}{4}) : y = - \frac{5}{16} x + \frac{5}{2}

y = - \frac{5}{16} x + \frac{5}{2}

x \to \infty lim (ln (x^{\frac{4}{x}}))

\int \frac{x ^{3} + 2}{x ^{2} - 1} d x

y^{^{'}} - \frac{8}{x} y = \frac{y ^{5}}{x ^{11}}

\int_{1}^{2} (2 x + x^{2}) d x

\int (\frac{1}{1 - x ^{2}}) d x

What is the tangent of f(x)= 5/x ,\at x=4 ?
The tangent of f(x)= 5/x ,\at x=4 is y=-5/16 x+5/2