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

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

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tangent of 7x-7sqrt(x)

tangent of

7 x - 7 x

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

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, 7 a_{0} - 7 a_{0})

Find the slope of

y = 7 x - 7 x : \frac{d y}{d x} = 7 - \frac{7}{2 x}

Compute the slope of

y = 7 x - 7 x

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

Find the line with slope m=

7 - \frac{7}{2 a _{0}}

and passing through

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

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

\frac{d}{d x} ((\frac{4 x + 1}{2 - 5 x})^{\frac{1}{3}})

f (x) = 5 x^{2} cos (x) - 4 x

y = arccos (2 x + 3)

\frac{1}{( s + 1 ) ( s - 1 ) ^{2}}

x y^{^{'}} - y = x^{2} + x - 2

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