What is the tangent of 4x-4sqrt(x) ?

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

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tangent of 4x-4sqrt(x)

tangent of

4 x - 4 x

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

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, 4 a_{0} - 4 a_{0})

Find the slope of

y = 4 x - 4 x : \frac{d y}{d x} = 4 - \frac{2}{x}

Compute the slope of

y = 4 x - 4 x

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

Find the line with slope m=

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

and passing through

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

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

f (x) = e^{8 x}

x \to \frac{x}{4} lim (tan (2 x))

\int cos (2 x) e^{3 x} d x

y = arctan (x)

\int 3 x - 4 d x

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