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} (x^{- 12})

x \to 2 lim (x^{2} - 4 x)

y (2 y^{2} - 3 x^{2}) d x + (2 x^{3}) d y = 0

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

\int (- 3 x^{4} + 6 x^{3} - 5 x^{2}) 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