What is the tangent of x^4-5x^3+2 ?

The tangent of x^4-5x^3+2 is y=(4a_{0}^3-15a_{0}^2)x-3a_{0}^4+10a_{0}^3+2

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tangent of x^4-5x^3+2

tangent of

x^{4} - 5 x^{3} + 2

y = (4 a_{0}^{3} - 15 a_{0}^{2}) x - 3 a_{0}^{4} + 10 a_{0}^{3} + 2

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, a_{0}^{4} - 5 a_{0}^{3} + 2)

Find the slope of

y = x^{4} - 5 x^{3} + 2 : \frac{d y}{d x} = 4 x^{3} - 15 x^{2}

Compute the slope of

y = x^{4} - 5 x^{3} + 2

x = a_{0} : m = 4 a_{0}^{3} - 15 a_{0}^{2}

Find the line with slope m=

4 a_{0}^{3} - 15 a_{0}^{2}

and passing through

(a_{0}, a_{0}^{4} - 5 a_{0}^{3} + 2) : y = (4 a_{0}^{3} - 15 a_{0}^{2}) x - 3 a_{0}^{4} + 10 a_{0}^{3} + 2

y = (4 a_{0}^{3} - 15 a_{0}^{2}) x - 3 a_{0}^{4} + 10 a_{0}^{3} + 2

\frac{\partial}{\partial x} (x^{2} y^{3})

(4, - 2), (1, 1)

\int (1 + x^{2}) 2 x d x

\int \frac{1}{x ^{2} 16 + 9 x ^{2}} d x

y^{^{''}} - 6 y = 9 t

What is the tangent of x^4-5x^3+2 ?
The tangent of x^4-5x^3+2 is y=(4a_{0}^3-15a_{0}^2)x-3a_{0}^4+10a_{0}^3+2