What is the tangent of f(x)=6x^3-6x^2+4 ?

The tangent of f(x)=6x^3-6x^2+4 is y=(18a_{0}^2-12a_{0})x-12a_{0}^3+6a_{0}^2+4

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tangent of f(x)=6x^3-6x^2+4

tangent of

f (x) = 6 x^{3} - 6 x^{2} + 4

y = (18 a_{0}^{2} - 12 a_{0}) x - 12 a_{0}^{3} + 6 a_{0}^{2} + 4

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, 6 a_{0}^{3} - 6 a_{0}^{2} + 4)

Find the slope of

f (x) = 6 x^{3} - 6 x^{2} + 4 : \frac{df ( x )}{d x} = 18 x^{2} - 12 x

Compute the slope of

f (x) = 6 x^{3} - 6 x^{2} + 4

x = a_{0} : m = 18 a_{0}^{2} - 12 a_{0}

Find the line with slope m=

18 a_{0}^{2} - 12 a_{0}

and passing through

(a_{0}, 6 a_{0}^{3} - 6 a_{0}^{2} + 4) : y = (18 a_{0}^{2} - 12 a_{0}) x - 12 a_{0}^{3} + 6 a_{0}^{2} + 4

y = (18 a_{0}^{2} - 12 a_{0}) x - 12 a_{0}^{3} + 6 a_{0}^{2} + 4

x \to 0 + lim (2 x^{s i n (3 x)})

\int x e^{5 x + π} d x

x \to - 8 lim (- \frac{3 x}{x + 8})

3 x^{3} 25 - x^{2}

\int_{6}^{8} \frac{70}{( x - 6 ) ^{3}} d x

What is the tangent of f(x)=6x^3-6x^2+4 ?
The tangent of f(x)=6x^3-6x^2+4 is y=(18a_{0}^2-12a_{0})x-12a_{0}^3+6a_{0}^2+4