What is the tangent of f(x)=x+4/x ,(4,5) ?

The tangent of f(x)=x+4/x ,(4,5) is y= 3/4 x+2

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tangent of f(x)=x+4/x ,(4,5)

tangent of

f (x) = x + \frac{4}{x}, (4, 5)

y = \frac{3}{4} x + 2

Solution steps

Find the slope of

f (x) = x + \frac{4}{x} : \frac{df ( x )}{d x} = 1 - \frac{4}{x ^{2}}

Compute the slope of

f (x) = x + \frac{4}{x}

(4, 5) : m = \frac{3}{4}

Find the line with slope m=

\frac{3}{4}

and passing through

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

y = \frac{3}{4} x + 2

\frac{\partial}{\partial x} (y sin (x y))

\frac{d}{d x} (- \frac{36}{( 1 + 6 x ) ^{2}})

\frac{d y}{d x} = \frac{9 x ^{2} - 6}{x ^{2}}

\frac{\partial}{\partial y} (x e^{y} - x^{5} + y - 3)

\frac{d}{d x} (\frac{x}{x ^{2} + y ^{2} + 1})

What is the tangent of f(x)=x+4/x ,(4,5) ?
The tangent of f(x)=x+4/x ,(4,5) is y= 3/4 x+2