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}}

Compute the slope of

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

x = a : 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}

f^{^{'}} (t) - f (t) = - 6 t

\int 10 w w d w

f (x) = (x + 2) e^{\frac{1}{x}}

\frac{d}{d x} (x (3 - x)^{2})

y^{^{'}} = e^{y - x}

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