What is the tangent of 3x-3sqrt(x) ?

The tangent of 3x-3sqrt(x) is y=(3-3/(2sqrt(a_{0))})x-3sqrt(a_{0)}+(3sqrt(a_{0)})/2

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tangent of 3x-3sqrt(x)

tangent of

3 x - 3 x

y = (3 - \frac{3}{2 a _{0}}) x - 3 a_{0} + \frac{3 a _{0}}{2}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, 3 a_{0} - 3 a_{0})

Find the slope of

y = 3 x - 3 x : \frac{d y}{d x} = 3 - \frac{3}{2 x}

Compute the slope of

y = 3 x - 3 x

x = a_{0} : m = 3 - \frac{3}{2 a _{0}}

Find the line with slope m=

3 - \frac{3}{2 a _{0}}

and passing through

(a_{0}, 3 a_{0} - 3 a_{0}) : y = (3 - \frac{3}{2 a _{0}}) x - 3 a_{0} + \frac{3 a _{0}}{2}

y = (3 - \frac{3}{2 a _{0}}) x - 3 a_{0} + \frac{3 a _{0}}{2}

\int \frac{2 1 + x ^{4}}{x ^{3}} d x

\int \frac{x}{( 1 - 3 x ^{2} )} d x

x^{^{''}} - x^{^{'}} = 0

y - 2 y^{^{''}} + y^{^{''''}} = 0

x \to - 2 lim (lo g_{2} (8))

What is the tangent of 3x-3sqrt(x) ?
The tangent of 3x-3sqrt(x) is y=(3-3/(2sqrt(a_{0))})x-3sqrt(a_{0)}+(3sqrt(a_{0)})/2