What is the tangent of 9x-2x^2 ?

The tangent of 9x-2x^2 is y=(9-4a_{0})x+2a_{0}^2

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tangent of 9x-2x^2

tangent of

9 x - 2 x^{2}

y = (9 - 4 a_{0}) x + 2 a_{0}^{2}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, 9 a_{0} - 2 a_{0}^{2})

Find the slope of

y = 9 x - 2 x^{2} : \frac{d y}{d x} = 9 - 4 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 = 9 - 4 a_{0}

Find the line with slope m=

9 - 4 a_{0}

and passing through

(a_{0}, 9 a_{0} - 2 a_{0}^{2}) : y = (9 - 4 a_{0}) x + 2 a_{0}^{2}

y = (9 - 4 a_{0}) x + 2 a_{0}^{2}

\frac{d}{d x} (2 tan (x) + 2 tan^{3} (x))

\frac{4 s - 1}{s ^{2} ( s + 1 ) ^{3}}

x \to + 5 lim (\frac{x + 1}{x - 5})

\frac{d}{d x} ((x)^{3 x})

\int \frac{1}{( 4 x + 1 ) ^{3}} d x

What is the tangent of 9x-2x^2 ?
The tangent of 9x-2x^2 is y=(9-4a_{0})x+2a_{0}^2