What is the tangent of f(x)=50sqrt(x)-5x ?

The tangent of f(x)=50sqrt(x)-5x is y=((25)/(sqrt(a_{0))}-5)x+25sqrt(a_{0)}

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tangent of f(x)=50sqrt(x)-5x

tangent of

f (x) = 50 x - 5 x

y = (\frac{25}{a _{0}} - 5) x + 25 a_{0}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, 50 a_{0} - 5 a_{0})

Find the slope of

f (x) = 50 x - 5 x : \frac{df ( x )}{d x} = \frac{25}{x} - 5

Compute the slope of

f (x) = 50 x - 5 x

x = a_{0} : m = \frac{25}{a _{0}} - 5

Find the line with slope m=

\frac{25}{a _{0}} - 5

and passing through

(a_{0}, 50 a_{0} - 5 a_{0}) : y = (\frac{25}{a _{0}} - 5) x + 25 a_{0}

y = (\frac{25}{a _{0}} - 5) x + 25 a_{0}

y^{^{''}} - 6 y^{^{'}} + 2 y = x e^{x}

\frac{\partial}{\partial y} (cos (y) e^{x} + \frac{2}{x})

x^{2} (x^{3} - 1)

x \to 0 lim (\frac{b - c}{x ^{a}})

4 + 6 x

What is the tangent of f(x)=50sqrt(x)-5x ?
The tangent of f(x)=50sqrt(x)-5x is y=((25)/(sqrt(a_{0))}-5)x+25sqrt(a_{0)}