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

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

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

tangent of

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

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

Solution steps

Find the tangent point:

(3, 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 = 3 : m = \frac{2}{3}

Find the line with slope m=

\frac{2}{3}

and passing through

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

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

(- 5.6) (- 2.5)

\frac{2}{7}

\frac{d}{d x} (tan (x) + cos^{2} (x) + sin^{2} (x) - 3)

\int \frac{x - 1}{2 x} d x

y = x^{3} - 9 x^{2} + 24 x - 15

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