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}

\frac{d}{d x} (\frac{4 x ^{3}}{9})

\int_{- 4}^{- 2} (x^{2} - 4) d x

5 x^{2} + x

y^{^{'}} = \frac{( x ^{2} + x y + y ^{2} )}{x ^{2}}

\int x sin (\frac{x}{2}) d x

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