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

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

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

tangent of

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

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

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

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

Find the slope of

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

Compute the slope of

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

x = a_{0} : m = 3 a_{0}^{2} - 2 a_{0}

Find the line with slope m=

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

and passing through

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

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

(1 + x)^{\frac{1}{2}}

\frac{\partial}{\partial x} (10 x y)

\int x^{7} ln (x) d x

\frac{d}{d x} (\frac{x}{( 1 - x ^{2} ) ^{\frac{3}{2}}})

\frac{\partial}{\partial x} (e^{5 x e^{y}})

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