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

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

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

tangent of

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

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

Solution steps

Find the tangent point:

(4, - \frac{1}{4})

Find the slope of

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

Compute the slope of

f (x) = - \frac{1}{x}

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

Find the line with slope m=

\frac{1}{16}

and passing through

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

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

x \to 4 lim (\frac{12 - 3 x}{x - 4})

y^{^{''}} - 8 y^{^{'}} + 13 y = 0, y (0) = 0, y^{^{'}} (0) = 7

\int \frac{1}{( sec ( x ) + tan ( x ) ) ^{2}} d x

\frac{\partial}{\partial y} (3 x e^{- \frac{1}{y ^{3}}})

\int_{115}^{150} \frac{75}{2 x ^{2}} d x

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