What is the tangent of 9x-6sqrt(x) ?

The tangent of 9x-6sqrt(x) is y=(9-3/(sqrt(a_{0))})x-3sqrt(a_{0)}

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tangent of 9x-6sqrt(x)

tangent of

9 x - 6 x

y = (9 - \frac{3}{a _{0}}) x - 3 a_{0}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, 9 a_{0} - 6 a_{0})

Find the slope of

y = 9 x - 6 x : \frac{d y}{d x} = 9 - \frac{3}{x}

Compute the slope of

y = 9 x - 6 x

x = a_{0} : m = 9 - \frac{3}{a _{0}}

Find the line with slope m=

9 - \frac{3}{a _{0}}

and passing through

(a_{0}, 9 a_{0} - 6 a_{0}) : y = (9 - \frac{3}{a _{0}}) x - 3 a_{0}

y = (9 - \frac{3}{a _{0}}) x - 3 a_{0}

- 3 x^{3}

x \to 0 lim (x^{2} - 1)

\int (3 x^{2} + 9)^{2} d x

f (r) = 4 π r^{2}

- 3 x^{\frac{1}{2}} + x^{\frac{3}{2}}, at x = 9

What is the tangent of 9x-6sqrt(x) ?
The tangent of 9x-6sqrt(x) is y=(9-3/(sqrt(a_{0))})x-3sqrt(a_{0)}