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

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

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tangent of 50sqrt(x)-5x

tangent of

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

y = 50 x - 5 x : \frac{d y}{d x} = \frac{25}{x} - 5

EN : T i tl e G e n er a l Eq u a t i o n Sl o p e A t P o in t 2 Eq : 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}

3 (d^{2} x)

n = 1 \sum \infty n^{- 2}

\frac{\partial}{\partial x} (5 x^{4} y^{3} + 2 x y)

y^{^{'}} + t^{2} y = 1

\int_{0}^{\infty} e^{\frac{- x ^{2}}{2}} d x

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