What is the tangent of x^4-3x^3+5 ?

The tangent of x^4-3x^3+5 is y=(4a_{0}^3-9a_{0}^2)x-3a_{0}^4+6a_{0}^3+5

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tangent of x^4-3x^3+5

tangent of

x^{4} - 3 x^{3} + 5

y = (4 a_{0}^{3} - 9 a_{0}^{2}) x - 3 a_{0}^{4} + 6 a_{0}^{3} + 5

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, a_{0}^{4} - 3 a_{0}^{3} + 5)

Find the slope of

y = x^{4} - 3 x^{3} + 5 : \frac{d y}{d x} = 4 x^{3} - 9 x^{2}

Compute the slope of

y = x^{4} - 3 x^{3} + 5

x = a_{0} : m = 4 a_{0}^{3} - 9 a_{0}^{2}

Find the line with slope m=

4 a_{0}^{3} - 9 a_{0}^{2}

and passing through

(a_{0}, a_{0}^{4} - 3 a_{0}^{3} + 5) : y = (4 a_{0}^{3} - 9 a_{0}^{2}) x - 3 a_{0}^{4} + 6 a_{0}^{3} + 5

y = (4 a_{0}^{3} - 9 a_{0}^{2}) x - 3 a_{0}^{4} + 6 a_{0}^{3} + 5

y = e^{\frac{8}{9} x}

\int t^{2} e^{- 12 t} d t

\int \frac{x ^{2} + x - 6}{x ^{2} - 4 x + 3} d x

\frac{\partial}{\partial x} (\frac{4 x + y}{x - y})

x \to - \infty lim (3^{4 x})

What is the tangent of x^4-3x^3+5 ?
The tangent of x^4-3x^3+5 is y=(4a_{0}^3-9a_{0}^2)x-3a_{0}^4+6a_{0}^3+5