What is the tangent of 4x^3-5x+3 ?

The tangent of 4x^3-5x+3 is y=(12a_{0}^2-5)x-8a_{0}^3+3

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tangent of 4x^3-5x+3

tangent of

4 x^{3} - 5 x + 3

y = (12 a_{0}^{2} - 5) x - 8 a_{0}^{3} + 3

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, 4 a_{0}^{3} - 5 a_{0} + 3)

Find the slope of

y = 4 x^{3} - 5 x + 3 : \frac{d y}{d x} = 12 x^{2} - 5

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 = 12 a_{0}^{2} - 5

Find the line with slope m=

12 a_{0}^{2} - 5

and passing through

(a_{0}, 4 a_{0}^{3} - 5 a_{0} + 3) : y = (12 a_{0}^{2} - 5) x - 8 a_{0}^{3} + 3

y = (12 a_{0}^{2} - 5) x - 8 a_{0}^{3} + 3

x \to 0 lim ((\frac{1}{x}) sin (x))

y = \frac{25}{2} - \frac{x ^{2}}{2}, (- 5, 5)

\frac{d}{d x} (5 - 3 x)

20 t^{3}

y = sin^{2} (x^{2})

What is the tangent of 4x^3-5x+3 ?
The tangent of 4x^3-5x+3 is y=(12a_{0}^2-5)x-8a_{0}^3+3