What is the tangent of x^3-x^2+1 ?

The tangent of x^3-x^2+1 is y=(3a_{0}^2-2a_{0})x-2a_{0}^3+a_{0}^2+1

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tangent of x^3-x^2+1

tangent of

x^{3} - x^{2} + 1

y = (3 a_{0}^{2} - 2 a_{0}) x - 2 a_{0}^{3} + a_{0}^{2} + 1

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} + 1)

Find the slope of

y = x^{3} - x^{2} + 1 : \frac{d y}{d x} = 3 x^{2} - 2 x

Compute the slope of

y = x^{3} - x^{2} + 1

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} + 1) : y = (3 a_{0}^{2} - 2 a_{0}) x - 2 a_{0}^{3} + a_{0}^{2} + 1

y = (3 a_{0}^{2} - 2 a_{0}) x - 2 a_{0}^{3} + a_{0}^{2} + 1

\int x \cdot ln (\frac{1 - x}{1 + x}) d x

\frac{d}{d x} ((ln (x + 1))^{2 - e^{x^{2}}})

\int_{1}^{2} \frac{x}{2} - \frac{2}{x} d x

x \to \frac{π}{3} lim (tan (3 x))

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

What is the tangent of x^3-x^2+1 ?
The tangent of x^3-x^2+1 is y=(3a_{0}^2-2a_{0})x-2a_{0}^3+a_{0}^2+1