What is the tangent of-6+250x^3-3x^5 ?

The tangent of-6+250x^3-3x^5 is y=(-15a_{0}^4+750a_{0}^2)x+12a_{0}^5-500a_{0}^3-6

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tangent of-6+250x^3-3x^5

tangent of

- 6 + 250 x^{3} - 3 x^{5}

y = (- 15 a_{0}^{4} + 750 a_{0}^{2}) x + 12 a_{0}^{5} - 500 a_{0}^{3} - 6

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, - 6 + 250 a_{0}^{3} - 3 a_{0}^{5})

Find the slope of

y = - 6 + 250 x^{3} - 3 x^{5} : \frac{d y}{d x} = - 15 x^{4} + 750 x^{2}

Compute the slope of

y = - 6 + 250 x^{3} - 3 x^{5}

x = a_{0} : m = - 15 a_{0}^{4} + 750 a_{0}^{2}

Find the line with slope m=

- 15 a_{0}^{4} + 750 a_{0}^{2}

and passing through

(a_{0}, - 6 + 250 a_{0}^{3} - 3 a_{0}^{5}) : y = (- 15 a_{0}^{4} + 750 a_{0}^{2}) x + 12 a_{0}^{5} - 500 a_{0}^{3} - 6

y = (- 15 a_{0}^{4} + 750 a_{0}^{2}) x + 12 a_{0}^{5} - 500 a_{0}^{3} - 6

y = 7 + 4 x^{2} - 2 x^{3}

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

\frac{x ^{2} - 3 x}{x + 1}

\frac{d}{d x} (\frac{1}{5 x + 1})

\int \frac{3 - 18 x}{49 - 9 x ^{2}} d x

What is the tangent of-6+250x^3-3x^5 ?
The tangent of-6+250x^3-3x^5 is y=(-15a_{0}^4+750a_{0}^2)x+12a_{0}^5-500a_{0}^3-6