What is the tangent of 7/(2sqrt(7x+2)) ?

The tangent of 7/(2sqrt(7x+2)) is y=-(49)/(4(7a_{0)+2)^{3/2}}x+(147a_{0}+28)/(4(7a_{0)+2)^{3/2}}

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tangent of 7/(2sqrt(7x+2))

tangent of

\frac{7}{2 7 x + 2}

y = - \frac{49}{4 ( 7 a _{0} + 2 ) ^{\frac{3}{2}}} x + \frac{147 a _{0} + 28}{4 ( 7 a _{0} + 2 ) ^{\frac{3}{2}}}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, \frac{7}{2 7 a _{0} + 2})

Find the slope of

y = \frac{7}{2 7 x + 2} : \frac{d y}{d x} = - \frac{49}{4 ( 7 x + 2 ) ^{\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{49}{4 ( 7 a _{0} + 2 ) ^{\frac{3}{2}}}

Find the line with slope m=

- \frac{49}{4 ( 7 a _{0} + 2 ) ^{\frac{3}{2}}}

and passing through

(a_{0}, \frac{7}{2 7 a _{0} + 2}) : y = - \frac{49}{4 ( 7 a _{0} + 2 ) ^{\frac{3}{2}}} x + \frac{147 a _{0} + 28}{4 ( 7 a _{0} + 2 ) ^{\frac{3}{2}}}

y = - \frac{49}{4 ( 7 a _{0} + 2 ) ^{\frac{3}{2}}} x + \frac{147 a _{0} + 28}{4 ( 7 a _{0} + 2 ) ^{\frac{3}{2}}}

What is the tangent of 7/(2sqrt(7x+2)) ?
The tangent of 7/(2sqrt(7x+2)) is y=-(49)/(4(7a_{0)+2)^{3/2}}x+(147a_{0}+28)/(4(7a_{0)+2)^{3/2}}