What is the tangent of f(x)=x^2-1/x ?

The tangent of f(x)=x^2-1/x is y=(2a_{0}+1/(a_{0)^2})x-2/(a_{0)}-a_{0}^2

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tangent of f(x)=x^2-1/x

tangent of

f (x) = x^{2} - \frac{1}{x}

y = (2 a_{0} + \frac{1}{a _{0}^{2}}) x - \frac{2}{a _{0}} - a_{0}^{2}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, a_{0}^{2} - \frac{1}{a _{0}})

Find the slope of

f (x) = x^{2} - \frac{1}{x} : \frac{df ( x )}{d x} = 2 x + \frac{1}{x ^{2}}

Compute the slope of

f (x) = x^{2} - \frac{1}{x}

x = a_{0} : m = 2 a_{0} + \frac{1}{a _{0}^{2}}

Find the line with slope m=

2 a_{0} + \frac{1}{a _{0}^{2}}

and passing through

(a_{0}, a_{0}^{2} - \frac{1}{a _{0}}) : y = (2 a_{0} + \frac{1}{a _{0}^{2}}) x - \frac{2}{a _{0}} - a_{0}^{2}

y = (2 a_{0} + \frac{1}{a _{0}^{2}}) x - \frac{2}{a _{0}} - a_{0}^{2}

\frac{d}{d x} (1 - \frac{1}{1 + x})

\frac{\partial}{\partial x} (\frac{4 x - 4 z}{3 y + 4 z})

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

\frac{3 s}{( s - 1 ) ( s ^{2} - 4 )}

\int \frac{( 6 x - 7 )}{3 x ^{2} - 7 x + 11} d x

What is the tangent of f(x)=x^2-1/x ?
The tangent of f(x)=x^2-1/x is y=(2a_{0}+1/(a_{0)^2})x-2/(a_{0)}-a_{0}^2