What is the tangent of y=x^3-2x^2+x+7 ?

The tangent of y=x^3-2x^2+x+7 is y=(3a_{0}^2-4a_{0}+1)x-2a_{0}^3+2a_{0}^2+7

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tangent of y=x^3-2x^2+x+7

tangent of

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

y = (3 a_{0}^{2} - 4 a_{0} + 1) x - 2 a_{0}^{3} + 2 a_{0}^{2} + 7

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, a_{0}^{3} - 2 a_{0}^{2} + a_{0} + 7)

Find the slope of

y = x^{3} - 2 x^{2} + x + 7 : \frac{d y}{d x} = 3 x^{2} - 4 x + 1

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 = 3 a_{0}^{2} - 4 a_{0} + 1

Find the line with slope m=

3 a_{0}^{2} - 4 a_{0} + 1

and passing through

(a_{0}, a_{0}^{3} - 2 a_{0}^{2} + a_{0} + 7) : y = (3 a_{0}^{2} - 4 a_{0} + 1) x - 2 a_{0}^{3} + 2 a_{0}^{2} + 7

y = (3 a_{0}^{2} - 4 a_{0} + 1) x - 2 a_{0}^{3} + 2 a_{0}^{2} + 7

What is the tangent of y=x^3-2x^2+x+7 ?
The tangent of y=x^3-2x^2+x+7 is y=(3a_{0}^2-4a_{0}+1)x-2a_{0}^3+2a_{0}^2+7