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

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

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tangent of sqrt(7x+4)

tangent of

7 x + 4

y = \frac{7}{2 7 a _{0} + 4} x + 7 a_{0} + 4 - \frac{7 a _{0}}{2 7 a _{0} + 4}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, 7 a_{0} + 4)

Find the slope of

y = 7 x + 4 : \frac{d y}{d x} = \frac{7}{2 7 x + 4}

Compute the slope of

y = 7 x + 4

x = a_{0} : m = \frac{7}{2 7 a _{0} + 4}

Find the line with slope m=

\frac{7}{2 7 a _{0} + 4}

and passing through

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

y = \frac{7}{2 7 a _{0} + 4} x + 7 a_{0} + 4 - \frac{7 a _{0}}{2 7 a _{0} + 4}

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