What is the tangent of 6x^2 ?

The tangent of 6x^2 is y=12a_{0}x-6a_{0}^2

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tangent of 6x^2

tangent of

6 x^{2}

y = 12 a_{0} x - 6 a_{0}^{2}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, 6 a_{0}^{2})

Find the slope of

y = 6 x^{2} : \frac{d y}{d x} = 12 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 = 12 a_{0}

Find the line with slope m=

12 a_{0}

and passing through

(a_{0}, 6 a_{0}^{2}) : y = 12 a_{0} x - 6 a_{0}^{2}

y = 12 a_{0} x - 6 a_{0}^{2}

(2 x + 1)^{2} (0.1)

x^{2} - 2 x, - x^{2} + 2 x

\int (e^{8 x} + 4 e^{- x}) d x

\int 7 x - 2 d x

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