What is the tangent of 3x^2 ?

The tangent of 3x^2 is y=6a_{0}x-3a_{0}^2

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tangent of 3x^2

tangent of

3 x^{2}

y = 6 a_{0} x - 3 a_{0}^{2}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, 3 a_{0}^{2})

Find the slope of

y = 3 x^{2} : \frac{d y}{d x} = 6 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 = 6 a_{0}

Find the line with slope m=

6 a_{0}

and passing through

(a_{0}, 3 a_{0}^{2}) : y = 6 a_{0} x - 3 a_{0}^{2}

y = 6 a_{0} x - 3 a_{0}^{2}

\int (8 x^{2} + 3 x^{4} + \frac{5}{2 x ^{8}} + e^{x}) d x

x y^{^{'}} - y = 2020 x^{2}, y (1) = 1

\int 12 sin^{3} (x co) s^{2} x d x

y^{^{'}} - \frac{1}{x} y = 9, y (1) = \frac{1}{7}

\int \frac{1}{( 1 + \frac{x}{2} ) ^{2}} d x