What is the tangent of f(x)=x+3/x ,\at x=4 ?

The tangent of f(x)=x+3/x ,\at x=4 is y= 13/16 x+3/2

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tangent of f(x)=x+3/x ,\at x=4

tangent of

f (x) = x + \frac{3}{x}, at x = 4

y = \frac{13}{16} x + \frac{3}{2}

Solution steps

Find the tangent point:

(4, \frac{19}{4})

Find the slope of

f (x) = x + \frac{3}{x} : \frac{df ( x )}{d x} = 1 - \frac{3}{x ^{2}}

Compute the slope of

f (x) = x + \frac{3}{x}

x = 4 : m = \frac{13}{16}

Find the line with slope m=

\frac{13}{16}

and passing through

(4, \frac{19}{4}) : y = \frac{13}{16} x + \frac{3}{2}

y = \frac{13}{16} x + \frac{3}{2}

\frac{d}{d x} (\frac{x ^{2}}{x + 4})

(15, 0), (0, - 2)

\int \frac{x ^{2}}{36 - x ^{2}} d x

\frac{d}{d x} (\frac{x}{5})

x \to 0 lim (x (13 + \frac{5}{x}))

What is the tangent of f(x)=x+3/x ,\at x=4 ?
The tangent of f(x)=x+3/x ,\at x=4 is y= 13/16 x+3/2