What is the tangent of 4/(sqrt(x-7)) ?

The tangent of 4/(sqrt(x-7)) is y=-2/((a_{0)-7)^{3/2}}x+(6a_{0}-28)/((a_{0)-7)^{3/2}}

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tangent of 4/(sqrt(x-7))

tangent of

\frac{4}{x - 7}

y = - \frac{2}{( a _{0} - 7 ) ^{\frac{3}{2}}} x + \frac{6 a _{0} - 28}{( a _{0} - 7 ) ^{\frac{3}{2}}}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, \frac{4}{a _{0} - 7})

Find the slope of

y = \frac{4}{x - 7} : \frac{d y}{d x} = - \frac{2}{( x - 7 ) ^{\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{2}{( a _{0} - 7 ) ^{\frac{3}{2}}}

Find the line with slope m=

- \frac{2}{( a _{0} - 7 ) ^{\frac{3}{2}}}

and passing through

(a_{0}, \frac{4}{a _{0} - 7}) : y = - \frac{2}{( a _{0} - 7 ) ^{\frac{3}{2}}} x + \frac{6 a _{0} - 28}{( a _{0} - 7 ) ^{\frac{3}{2}}}

y = - \frac{2}{( a _{0} - 7 ) ^{\frac{3}{2}}} x + \frac{6 a _{0} - 28}{( a _{0} - 7 ) ^{\frac{3}{2}}}

What is the tangent of 4/(sqrt(x-7)) ?
The tangent of 4/(sqrt(x-7)) is y=-2/((a_{0)-7)^{3/2}}x+(6a_{0}-28)/((a_{0)-7)^{3/2}}