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}}

EN : T i tl e G e n er a l Eq u a t i o n Sl o p e A t P o in t 2 Eq : 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}

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