What is the tangent of f(x)=x^3-5x^2 ?

The tangent of f(x)=x^3-5x^2 is y=(3a_{0}^2-10a_{0})x-2a_{0}^3+5a_{0}^2

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tangent of f(x)=x^3-5x^2

tangent of

f (x) = x^{3} - 5 x^{2}

y = (3 a_{0}^{2} - 10 a_{0}) x - 2 a_{0}^{3} + 5 a_{0}^{2}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, a_{0}^{3} - 5 a_{0}^{2})

Find the slope of

f (x) = x^{3} - 5 x^{2} : \frac{df ( x )}{d x} = 3 x^{2} - 10 x

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} - 10 a_{0}

Find the line with slope m=

3 a_{0}^{2} - 10 a_{0}

and passing through

(a_{0}, a_{0}^{3} - 5 a_{0}^{2}) : y = (3 a_{0}^{2} - 10 a_{0}) x - 2 a_{0}^{3} + 5 a_{0}^{2}

y = (3 a_{0}^{2} - 10 a_{0}) x - 2 a_{0}^{3} + 5 a_{0}^{2}

What is the tangent of f(x)=x^3-5x^2 ?
The tangent of f(x)=x^3-5x^2 is y=(3a_{0}^2-10a_{0})x-2a_{0}^3+5a_{0}^2