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

The tangent of f(x)= 1/(x-2),\at x=4 is y=-1/4 x+3/2

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tangent of f(x)= 1/(x-2),\at x=4

tangent of

f (x) = \frac{1}{x - 2}, at x = 4

y = - \frac{1}{4} x + \frac{3}{2}

Solution steps

Find the tangent point:

(4, \frac{1}{2})

Find the slope of

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

EN : T i tl e G e n er a l Eq u a t i o n Sl o p e A t P o in t 2 Eq : m = - \frac{1}{4}

Find the line with slope m=

- \frac{1}{4}

and passing through

(4, \frac{1}{2}) : y = - \frac{1}{4} x + \frac{3}{2}

y = - \frac{1}{4} x + \frac{3}{2}

(\frac{19}{2}, - \frac{5}{3}), (- \frac{3}{2}, - \frac{7}{24})

\int \frac{sec ( x ) tan ( x )}{sec ( x ) - 4} d x

y^{^{''}} + 4 y^{^{'}} + 4 y = 0, y (0) = 2, y^{^{'}} (0) = 4

\int \frac{1}{( 1 - t ) ^{2}} d t

\frac{d}{d x} (3 sin (6 x))

What is the tangent of f(x)= 1/(x-2),\at x=4 ?
The tangent of f(x)= 1/(x-2),\at x=4 is y=-1/4 x+3/2