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

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

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

tangent of

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

y = - \frac{1}{a ^{2}} x + \frac{2}{a}

Solution steps

Find the tangent point:

(a, \frac{1}{a})

Find the slope of

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

Find the line with slope m=

- \frac{1}{a ^{2}}

and passing through

(a, \frac{1}{a}) : y = - \frac{1}{a ^{2}} x + \frac{2}{a}

y = - \frac{1}{a ^{2}} x + \frac{2}{a}

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