What is the tangent of 7/(2sqrt(7x+2)),\at a=2 ?

The tangent of 7/(2sqrt(7x+2)),\at a=2 is y=-(49)/(4(7a+2)^{3/2)}x+(147a+28)/(4(7a+2)^{3/2)}

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tangent of 7/(2sqrt(7x+2)),\at a=2

tangent of

\frac{7}{2 7 x + 2}, at a = 2

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

Solution steps

Compute the tangent line to the general point

x = a

Find the tangent point:

(a, \frac{7}{2 7 a + 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}}}

Compute the slope of

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

x = a : m = - \frac{49}{4 ( 7 a + 2 ) ^{\frac{3}{2}}}

Find the line with slope m=

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

and passing through

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

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

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