What is the tangent of y=5x^3-5x ?

The tangent of y=5x^3-5x is y=(15a_{0}^2-5)x-10a_{0}^3

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tangent of y=5x^3-5x

tangent of

y = 5 x^{3} - 5 x

y = (15 a_{0}^{2} - 5) x - 10 a_{0}^{3}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, 5 a_{0}^{3} - 5 a_{0})

Find the slope of

y = 5 x^{3} - 5 x : \frac{d y}{d x} = 15 x^{2} - 5

Compute the slope of

y = 5 x^{3} - 5 x

x = a_{0} : m = 15 a_{0}^{2} - 5

Find the line with slope m=

15 a_{0}^{2} - 5

and passing through

(a_{0}, 5 a_{0}^{3} - 5 a_{0}) : y = (15 a_{0}^{2} - 5) x - 10 a_{0}^{3}

y = (15 a_{0}^{2} - 5) x - 10 a_{0}^{3}

y^{^{''}} - a^{2} y = 0

\int_{0}^{2} e^{2 t} d t

3 - x^{2}, - 1

y^{^{''}} + 4 y^{^{'}} + 25 y = 0

n = 1 \sum \infty \frac{5 n}{n ^{2} + 4}

What is the tangent of y=5x^3-5x ?
The tangent of y=5x^3-5x is y=(15a_{0}^2-5)x-10a_{0}^3