What is the tangent of y=3x-7sqrt(x) ?

The tangent of y=3x-7sqrt(x) is y=(3-7/(2sqrt(a_{0))})x-7sqrt(a_{0)}+(7sqrt(a_{0)})/2

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tangent of y=3x-7sqrt(x)

tangent of

y = 3 x - 7 x

y = (3 - \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}, 3 a_{0} - 7 a_{0})

Find the slope of

y = 3 x - 7 x : \frac{d y}{d x} = 3 - \frac{7}{2 x}

Compute the slope of

y = 3 x - 7 x

x = a_{0} : m = 3 - \frac{7}{2 a _{0}}

Find the line with slope m=

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

and passing through

(a_{0}, 3 a_{0} - 7 a_{0}) : y = (3 - \frac{7}{2 a _{0}}) x - 7 a_{0} + \frac{7 a _{0}}{2}

y = (3 - \frac{7}{2 a _{0}}) x - 7 a_{0} + \frac{7 a _{0}}{2}

x + 4 y + 2 x y

\int 4 x + 10 d x

y^{^{'}} - 4 y = - 3 e^{3 t}, y (0) = 9

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

x \to 0 lim (\frac{- cos ( x )}{x})

What is the tangent of y=3x-7sqrt(x) ?
The tangent of y=3x-7sqrt(x) is y=(3-7/(2sqrt(a_{0))})x-7sqrt(a_{0)}+(7sqrt(a_{0)})/2