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

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

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tangent of f(x)=2sqrt(x)-x

tangent of

f (x) = 2 x - x

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

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

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

Find the slope of

f (x) = 2 x - x : \frac{df ( x )}{d x} = \frac{1}{x} - 1

Compute the slope of

f (x) = 2 x - x

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

Find the line with slope m=

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

and passing through

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

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

\int_{0}^{2 - 2 x} 1 + 3 x + y d y

\int (5 x^{2} + 1) (5 x^{3} + 3 x - 8)^{6} d x

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

4 y^{2} + 7 x^{2}

\frac{\partial}{\partial x} (2 x y^{6} + x^{4} y^{8})

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