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

The tangent of f(x)=3x+2/x ,\at x=2 is y= 5/2 x+2

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

tangent of

f (x) = 3 x + \frac{2}{x}, at x = 2

y = \frac{5}{2} x + 2

Solution steps

Find the tangent point:

(2, 7)

Find the slope of

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

Compute the slope of

f (x) = 3 x + \frac{2}{x}

x = 2 : m = \frac{5}{2}

Find the line with slope m=

\frac{5}{2}

and passing through

(2, 7) : y = \frac{5}{2} x + 2

y = \frac{5}{2} x + 2

\frac{d y}{d x} + 7 x^{6} y = x^{6}

\frac{2 x + 4 x ^{2}}{( 1 + 4 x ) ^{2}}

\frac{d}{d x} (e^{k^{2} x})

\frac{d}{d x} (\frac{( x + 4 ) ^{2}}{x + 3})

(x^{2} + 1) y^{^{''}} + 2 x y^{^{'}} = 0

What is the tangent of f(x)=3x+2/x ,\at x=2 ?
The tangent of f(x)=3x+2/x ,\at x=2 is y= 5/2 x+2