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

Compute the slope of

y = - 3 x^{2}

x = a_{0} : 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}

\frac{d}{d x} (\frac{4}{4 x + 1})

\int \frac{4 + 8 x}{1 + x ^{2}} d x

\int 9 x^{2} + 4 x - 3 d x

\frac{d}{d x} (\frac{2 x - x ^{2}}{x} - 3 cot (x))

x \to 4 lim (2 x^{2} + 7)