What is the tangent of f(x)= 1/(2sqrt(x)),\at x=81 ?

The tangent of f(x)= 1/(2sqrt(x)),\at x=81 is y=-1/2916 x+1/12

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tangent of f(x)= 1/(2sqrt(x)),\at x=81

tangent of

f (x) = \frac{1}{2 x}, at x = 81

y = - \frac{1}{2916} x + \frac{1}{12}

Solution steps

Find the tangent point:

(81, \frac{1}{18})

Find the slope of

f (x) = \frac{1}{2 x} : \frac{df ( x )}{d x} = - \frac{1}{4 x ^{\frac{3}{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}{2916}

Find the line with slope m=

- \frac{1}{2916}

and passing through

(81, \frac{1}{18}) : y = - \frac{1}{2916} x + \frac{1}{12}

y = - \frac{1}{2916} x + \frac{1}{12}

What is the tangent of f(x)= 1/(2sqrt(x)),\at x=81 ?
The tangent of f(x)= 1/(2sqrt(x)),\at x=81 is y=-1/2916 x+1/12