What is the tangent of y=6x-x^2(1.5) ?

The tangent of y=6x-x^2(1.5) is y=(6-3a_{0})x+(3a_{0}^2)/2

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tangent of y=6x-x^2(1.5)

tangent of

y = 6 x - x^{2} (1.5)

y = (6 - 3 a_{0}) x + \frac{3 a _{0}^{2}}{2}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, 6 a_{0} - a_{0}^{2} \cdot 1.5)

Find the slope of

y = 6 x - x^{2} 1.5 : \frac{d y}{d x} = 6 - 3 x

Compute the slope of

y = 6 x - x^{2} 1.5

x = a_{0} : m = 6 - 3 a_{0}

Find the line with slope m=

6 - 3 a_{0}

and passing through

(a_{0}, 6 a_{0} - a_{0}^{2} 1.5) : y = (6 - 3 a_{0}) x + \frac{3 a _{0}^{2}}{2}

y = (6 - 3 a_{0}) x + \frac{3 a _{0}^{2}}{2}

\frac{d}{d x} (x^{2} lo g_{e} (2 x))

\frac{d y}{d x} + 4 tan (4 x) y = 3 cos (4 x)

(0, 1), (4, - 5)

\frac{1 + x ^{2}}{( 1 - x ^{2} ) ^{2}}

\frac{d}{d x} (ln (4 - x))

What is the tangent of y=6x-x^2(1.5) ?
The tangent of y=6x-x^2(1.5) is y=(6-3a_{0})x+(3a_{0}^2)/2