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

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

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tangent of 5/x ,\at x=4

tangent of

\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

y = \frac{5}{x} : \frac{d y}{d x} = - \frac{5}{x ^{2}}

Compute the slope of

y = \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}

\frac{d y}{d x} = \frac{3 x + 2 y + 1}{3 x + 2 y - 1}

f (x) = (4 x^{2} - 8 x + 8) e^{x}

\frac{\partial}{\partial y} (x e^{2 y} sin (7 z))

24 x - 0.01 x^{2}

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