What is the tangent of f(x)=x+1/x ,\at x=4 ?

The tangent of f(x)=x+1/x ,\at x=4 is y= 15/16 x+1/2

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tangent of f(x)=x+1/x ,\at x=4

tangent of

f (x) = x + \frac{1}{x}, at x = 4

y = \frac{15}{16} x + \frac{1}{2}

Solution steps

Find the tangent point:

(4, \frac{17}{4})

Find the slope of

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

Compute the slope of

f (x) = x + \frac{1}{x}

x = 4 : m = \frac{15}{16}

Find the line with slope m=

\frac{15}{16}

and passing through

(4, \frac{17}{4}) : y = \frac{15}{16} x + \frac{1}{2}

y = \frac{15}{16} x + \frac{1}{2}

\frac{d}{d x} (7 x^{6})

x \to 0 lim (\frac{( sin ( 3 x ) )}{x})

x^{2} y^{^{''}} - 5 x y^{^{'}} + 9 y = 0

x \to 2 lim (x^{2} - 7 x + 5)

\frac{\partial}{\partial x} (\frac{1}{x ^{2} + y ^{2} + 1})

What is the tangent of f(x)=x+1/x ,\at x=4 ?
The tangent of f(x)=x+1/x ,\at x=4 is y= 15/16 x+1/2