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

The tangent of 5x^3-3x^5 is y=(15a_{0}^2-15a_{0}^4)x+12a_{0}^5-10a_{0}^3

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tangent of 5x^3-3x^5

tangent of

5 x^{3} - 3 x^{5}

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

Find the slope of

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

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 = 15 a_{0}^{2} - 15 a_{0}^{4}

Find the line with slope m=

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

and passing through

(a_{0}, 5 a_{0}^{3} - 3 a_{0}^{5}) : y = (15 a_{0}^{2} - 15 a_{0}^{4}) x + 12 a_{0}^{5} - 10 a_{0}^{3}

y = (15 a_{0}^{2} - 15 a_{0}^{4}) x + 12 a_{0}^{5} - 10 a_{0}^{3}

What is the tangent of 5x^3-3x^5 ?
The tangent of 5x^3-3x^5 is y=(15a_{0}^2-15a_{0}^4)x+12a_{0}^5-10a_{0}^3