What is the tangent of f(x)= 1/x+4,\at x=-4 ?

The tangent of f(x)= 1/x+4,\at x=-4 is y=-1/16 x+7/2

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tangent of f(x)= 1/x+4,\at x=-4

tangent of

f (x) = \frac{1}{x} + 4, at x = - 4

y = - \frac{1}{16} x + \frac{7}{2}

Solution steps

Find the tangent point:

(- 4, \frac{15}{4})

Find the slope of

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

Compute the slope of

f (x) = \frac{1}{x} + 4

x = - 4 : m = - \frac{1}{16}

Find the line with slope m=

- \frac{1}{16}

and passing through

(- 4, \frac{15}{4}) : y = - \frac{1}{16} x + \frac{7}{2}

y = - \frac{1}{16} x + \frac{7}{2}

\frac{d y}{d x} + \frac{- x}{x + 1} = 0

\frac{d y}{d x} = - \frac{x y}{y - 1}

y = x^{2}, y = 8 + x

\int 100 t^{2} + 36 t^{4} d t

9 \frac{d}{d x} (\frac{d y}{d x}) + 10 y = 0

What is the tangent of f(x)= 1/x+4,\at x=-4 ?
The tangent of f(x)= 1/x+4,\at x=-4 is y=-1/16 x+7/2