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

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

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tangent of x+1/x ,\at x=4

tangent of

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

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

Compute the slope of

y = 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}

\int ln^{2} (c) os x tan (x)

\frac{d y}{d x} + y = x y^{3}

x \to 22 lim (2 x^{2} - 3 x - 5)

n = 1 \sum \infty \frac{3}{3 ^{n}}

n = 0 \sum \infty \frac{1}{n}

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