What is the tangent of 5x-2sqrt(x) ?

The tangent of 5x-2sqrt(x) is y=(5-1/(sqrt(a_{0))})x-sqrt(a_{0)}

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tangent of 5x-2sqrt(x)

tangent of

5 x - 2 x

y = (5 - \frac{1}{a _{0}}) x - a_{0}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, 5 a_{0} - 2 a_{0})

Find the slope of

y = 5 x - 2 x : \frac{d y}{d x} = 5 - \frac{1}{x}

Compute the slope of

y = 5 x - 2 x

x = a_{0} : m = 5 - \frac{1}{a _{0}}

Find the line with slope m=

5 - \frac{1}{a _{0}}

and passing through

(a_{0}, 5 a_{0} - 2 a_{0}) : y = (5 - \frac{1}{a _{0}}) x - a_{0}

y = (5 - \frac{1}{a _{0}}) x - a_{0}

y^{^{'}} + 3 y = 8, y (0) = 0

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

\int \frac{5 x + 8}{x ^{2} + 4 x + 4} d x

x \to \infty lim ((1 + \frac{1}{2 x})^{3 x})

\int_{2}^{6} t^{3} ln (4 t) d t

What is the tangent of 5x-2sqrt(x) ?
The tangent of 5x-2sqrt(x) is y=(5-1/(sqrt(a_{0))})x-sqrt(a_{0)}