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

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

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tangent of f(x)=4x-4sqrt(x)

tangent of

f (x) = 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

f (x) = 4 x - 4 x : \frac{df ( x )}{d x} = 4 - \frac{2}{x}

Compute the slope of

f (x) = 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}

\frac{\partial}{\partial x} (cos (- x))

\frac{d}{d x} (14 - x)

\int \frac{1}{( x + 3 ) x ^{2} + 6 x - 7} d x

\int 0.0015 x^{2} d x

\frac{\partial}{\partial x} (\frac{y x}{y + x})

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