What is the tangent of 7x-4x^2 ?

The tangent of 7x-4x^2 is y=(7-8a_{0})x+4a_{0}^2

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tangent of 7x-4x^2

tangent of

7 x - 4 x^{2}

y = (7 - 8 a_{0}) x + 4 a_{0}^{2}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, 7 a_{0} - 4 a_{0}^{2})

Find the slope of

y = 7 x - 4 x^{2} : \frac{d y}{d x} = 7 - 8 x

Compute the slope of

y = 7 x - 4 x^{2}

x = a_{0} : m = 7 - 8 a_{0}

Find the line with slope m=

7 - 8 a_{0}

and passing through

(a_{0}, 7 a_{0} - 4 a_{0}^{2}) : y = (7 - 8 a_{0}) x + 4 a_{0}^{2}

y = (7 - 8 a_{0}) x + 4 a_{0}^{2}

y^{^{'}} = y (4 - t y)

\frac{d}{d x} (cos^{2} (x) + sin^{2} (x))

\int x^{2} cos (8 x) d x

What is the tangent of 7x-4x^2 ?
The tangent of 7x-4x^2 is y=(7-8a_{0})x+4a_{0}^2