What is the tangent of 200x-0.1x^{(2)} ?

The tangent of 200x-0.1x^{(2)} is y=(200-0.2a_{0})x+0.1a_{0}^2

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tangent of 200x-0.1x^{(2)}

tangent of

200 x - 0.1 x^{(2)}

y = (200 - 0.2 a_{0}) x + 0.1 a_{0}^{2}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, 200 a_{0} - 0.1 a_{0}^{2})

Find the slope of

y = 200 x - 0.1 x^{2} : \frac{d y}{d x} = 200 - 0.2 x

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 = 200 - 0.2 a_{0}

Find the line with slope m=

200 - 0.2 a_{0}

and passing through

(a_{0}, 200 a_{0} - 0.1 a_{0}^{2}) : y = (200 - 0.2 a_{0}) x + 0.1 a_{0}^{2}

y = (200 - 0.2 a_{0}) x + 0.1 a_{0}^{2}

x \to - 1 lim (\frac{3}{2} - \frac{1}{2} x^{2})

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

100 y^{^{''}} - 80 y^{^{'}} + 20 y = 0, y (3) = 3, y^{^{'}} (3) = 8

\int_{0}^{0.5} - \frac{1}{10} e^{- 10 y} d y

lo g_{100} (x), (0, 24)

What is the tangent of 200x-0.1x^{(2)} ?
The tangent of 200x-0.1x^{(2)} is y=(200-0.2a_{0})x+0.1a_{0}^2