What is the tangent of-3x^2+6x-2 ?

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

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tangent of-3x^2+6x-2

tangent of

- 3 x^{2} + 6 x - 2

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

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, - 3 a_{0}^{2} + 6 a_{0} - 2)

Find the slope of

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

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} + 6

Find the line with slope m=

- 6 a_{0} + 6

and passing through

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

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

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

f^{^{'}} (x) = sec (2 x) tan (2 x)

\frac{d y}{d x} = 2 y (3 - x)

\int \frac{x ^{2}}{x ^{2} - 3 x + 2} d x

x \to 4 lim (\frac{1}{x ^{2} - 16})

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