What is the tangent of 2x^3-3x^2-72x+2 ?

The tangent of 2x^3-3x^2-72x+2 is y=(6a_{0}^2-6a_{0}-72)x-4a_{0}^3+3a_{0}^2+2

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tangent of 2x^3-3x^2-72x+2

tangent of

2 x^{3} - 3 x^{2} - 72 x + 2

y = (6 a_{0}^{2} - 6 a_{0} - 72) x - 4 a_{0}^{3} + 3 a_{0}^{2} + 2

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, 2 a_{0}^{3} - 3 a_{0}^{2} - 72 a_{0} + 2)

Find the slope of

y = 2 x^{3} - 3 x^{2} - 72 x + 2 : \frac{d y}{d x} = 6 x^{2} - 6 x - 72

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 = 6 a_{0}^{2} - 6 a_{0} - 72

Find the line with slope m=

6 a_{0}^{2} - 6 a_{0} - 72

and passing through

(a_{0}, 2 a_{0}^{3} - 3 a_{0}^{2} - 72 a_{0} + 2) : y = (6 a_{0}^{2} - 6 a_{0} - 72) x - 4 a_{0}^{3} + 3 a_{0}^{2} + 2

y = (6 a_{0}^{2} - 6 a_{0} - 72) x - 4 a_{0}^{3} + 3 a_{0}^{2} + 2

\frac{s + 1}{s ^{2} - 4 s}

2 \cdot e^{x^{2} - 4 x}

\int 2 x - 5 d x

\int 8 x ln (3 x) d x

\frac{d}{d x} (x ln (x^{2} + 4) + 4 arctan (\frac{x}{2}) - 2 x)

What is the tangent of 2x^3-3x^2-72x+2 ?
The tangent of 2x^3-3x^2-72x+2 is y=(6a_{0}^2-6a_{0}-72)x-4a_{0}^3+3a_{0}^2+2