What is the tangent of f(x)= 4/x ?

The tangent of f(x)= 4/x is y=-4/(a_{0)^2}x+8/(a_{0)}

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tangent of f(x)= 4/x

tangent of

f (x) = \frac{4}{x}

y = - \frac{4}{a _{0}^{2}} x + \frac{8}{a _{0}}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, \frac{4}{a _{0}})

Find the slope of

f (x) = \frac{4}{x} : \frac{df ( x )}{d x} = - \frac{4}{x ^{2}}

Compute the slope of

f (x) = \frac{4}{x}

x = a_{0} : m = - \frac{4}{a _{0}^{2}}

Find the line with slope m=

- \frac{4}{a _{0}^{2}}

and passing through

(a_{0}, \frac{4}{a _{0}}) : y = - \frac{4}{a _{0}^{2}} x + \frac{8}{a _{0}}

y = - \frac{4}{a _{0}^{2}} x + \frac{8}{a _{0}}

\int (x^{2} + 2 x) \cdot cos (x) d x

\int x^{2} e^{- x^{2}} d x

\int (4 x^{3} - 3 x^{2} + 2 x - 5) d x

\frac{d}{d x} (f (\frac{1}{3} x^{3})) = 2 x^{5}

What is the tangent of f(x)= 4/x ?
The tangent of f(x)= 4/x is y=-4/(a_{0)^2}x+8/(a_{0)}