What is the tangent of x^3-8x^2+5x-2 ?

The tangent of x^3-8x^2+5x-2 is y=(3a_{0}^2-16a_{0}+5)x-2a_{0}^3+8a_{0}^2-2

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tangent of x^3-8x^2+5x-2

tangent of

x^{3} - 8 x^{2} + 5 x - 2

y = (3 a_{0}^{2} - 16 a_{0} + 5) x - 2 a_{0}^{3} + 8 a_{0}^{2} - 2

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, a_{0}^{3} - 8 a_{0}^{2} + 5 a_{0} - 2)

Find the slope of

y = x^{3} - 8 x^{2} + 5 x - 2 : \frac{d y}{d x} = 3 x^{2} - 16 x + 5

Compute the slope of

y = x^{3} - 8 x^{2} + 5 x - 2

x = a_{0} : m = 3 a_{0}^{2} - 16 a_{0} + 5

Find the line with slope m=

3 a_{0}^{2} - 16 a_{0} + 5

and passing through

(a_{0}, a_{0}^{3} - 8 a_{0}^{2} + 5 a_{0} - 2) : y = (3 a_{0}^{2} - 16 a_{0} + 5) x - 2 a_{0}^{3} + 8 a_{0}^{2} - 2

y = (3 a_{0}^{2} - 16 a_{0} + 5) x - 2 a_{0}^{3} + 8 a_{0}^{2} - 2

\frac{\partial}{\partial x} (4 e^{x y + 3})

(7 x^{6} + 2 x^{3})^{4}

x + 8

n = 0 \sum \infty 3^{n} 7^{- n}

\frac{\partial}{\partial y} (- x y^{2})

What is the tangent of x^3-8x^2+5x-2 ?
The tangent of x^3-8x^2+5x-2 is y=(3a_{0}^2-16a_{0}+5)x-2a_{0}^3+8a_{0}^2-2