What is the tangent of f(x)=3x^2-2x ?

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

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tangent of f(x)=3x^2-2x

tangent of

f (x) = 3 x^{2} - 2 x

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

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

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

Find the slope of

f (x) = 3 x^{2} - 2 x : \frac{df ( x )}{d x} = 6 x - 2

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

Find the line with slope m=

6 a_{0} - 2

and passing through

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

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

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