What is the tangent of-4-9x^2 ?

The tangent of-4-9x^2 is y=-18a_{0}x-4+9a_{0}^2

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tangent of-4-9x^2

tangent of

- 4 - 9 x^{2}

y = - 18 a_{0} x - 4 + 9 a_{0}^{2}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, - 4 - 9 a_{0}^{2})

Find the slope of

y = - 4 - 9 x^{2} : \frac{d y}{d x} = - 18 x

Compute the slope of

y = - 4 - 9 x^{2}

x = a_{0} : m = - 18 a_{0}

Find the line with slope m=

- 18 a_{0}

and passing through

(a_{0}, - 4 - 9 a_{0}^{2}) : y = - 18 a_{0} x - 4 + 9 a_{0}^{2}

y = - 18 a_{0} x - 4 + 9 a_{0}^{2}

2 \frac{d ^{2} y}{d x ^{2}} + 11 \frac{d y}{d x} - 6 y = 8 x

(x^{2} - 4) \frac{d y}{d x} + 4 y = (x + 2)^{2}

x \to 2 lim (x^{3} + 5 x^{2} - 7 x + 1)

\frac{d}{d x} (- \frac{25}{( 1 + 5 x ) ^{2}})

\frac{x}{5} + \frac{5}{x}