What is the tangent of f(x)= 1/(sqrt(7x)),\at x=9 ?

The tangent of f(x)= 1/(sqrt(7x)),\at x=9 is y=-1/(54sqrt(7))x+1/(2sqrt(7))

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tangent of f(x)= 1/(sqrt(7x)),\at x=9

tangent of

f (x) = \frac{1}{7 x}, at x = 9

y = - \frac{1}{54 7} x + \frac{1}{2 7}

Solution steps

Find the tangent point:

(9, \frac{1}{3 7})

Find the slope of

f (x) = \frac{1}{7 x} : \frac{df ( x )}{d x} = - \frac{1}{2 7 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}{54 7}

Find the line with slope m=

- \frac{1}{54 7}

and passing through

(9, \frac{1}{3 7}) : y = - \frac{1}{54 7} x + \frac{1}{2 7}

y = - \frac{1}{54 7} x + \frac{1}{2 7}

What is the tangent of f(x)= 1/(sqrt(7x)),\at x=9 ?
The tangent of f(x)= 1/(sqrt(7x)),\at x=9 is y=-1/(54sqrt(7))x+1/(2sqrt(7))