What is the tangent of f(x)=x^3,a ?

The tangent of f(x)=x^3,a is y=3a^2x-2a^3

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tangent of f(x)=x^3,a

tangent of

f (x) = x^{3}, a

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

Solution steps

Compute the tangent line to the general point

x = a

Find the tangent point:

(a, a^{3})

Find the slope of

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

Find the line with slope m=

3 a^{2}

and passing through

(a, a^{3}) : y = 3 a^{2} x - 2 a^{3}

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