What is the tangent of f(x)= 3/x ,\at x=-4 ?

The tangent of f(x)= 3/x ,\at x=-4 is y=-3/16 x-3/2

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tangent of f(x)= 3/x ,\at x=-4

tangent of

f (x) = \frac{3}{x}, at x = - 4

y = - \frac{3}{16} x - \frac{3}{2}

Solution steps

Find the tangent point:

(- 4, - \frac{3}{4})

Find the slope of

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

Compute the slope of

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

x = - 4 : m = - \frac{3}{16}

Find the line with slope m=

- \frac{3}{16}

and passing through

(- 4, - \frac{3}{4}) : y = - \frac{3}{16} x - \frac{3}{2}

y = - \frac{3}{16} x - \frac{3}{2}

\int \frac{5 + x + x}{x} d x

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

x \to 2 lim (x^{2} - 2 x + 4)

\int cos (y x) d x

x \frac{d y}{d x} + 2 y = x^{- 3}

What is the tangent of f(x)= 3/x ,\at x=-4 ?
The tangent of f(x)= 3/x ,\at x=-4 is y=-3/16 x-3/2