What is the tangent of (8x-x^2)(1.7) ?

The tangent of (8x-x^2)(1.7) is y=1.7(8-2a_{0})x+(17a_{0}^2)/(10)

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tangent of (8x-x^2)(1.7)

tangent of

(8 x - x^{2}) (1.7)

y = 1.7 (8 - 2 a_{0}) x + \frac{17 a _{0}^{2}}{10}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, (8 a_{0} - a_{0}^{2}) \cdot 1.7)

Find the slope of

y = (8 x - x^{2}) 1.7 : \frac{d y}{d x} = 1.7 (8 - 2 x)

Compute the slope of

y = (8 x - x^{2}) 1.7

x = a_{0} : m = 1.7 (8 - 2 a_{0})

Find the line with slope m=

1.7 (8 - 2 a_{0})

and passing through

(a_{0}, (8 a_{0} - a_{0}^{2}) 1.7) : y = 1.7 (8 - 2 a_{0}) x + \frac{17 a _{0}^{2}}{10}

y = 1.7 (8 - 2 a_{0}) x + \frac{17 a _{0}^{2}}{10}

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What is the tangent of (8x-x^2)(1.7) ?
The tangent of (8x-x^2)(1.7) is y=1.7(8-2a_{0})x+(17a_{0}^2)/(10)