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

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

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

tangent of

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

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

Find the slope of

y = x^{4} - 3 x^{2} + 2 : \frac{d y}{d x} = 4 x^{3} - 6 x

Compute the slope of

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

x = a_{0} : m = 4 a_{0}^{3} - 6 a_{0}

Find the line with slope m=

4 a_{0}^{3} - 6 a_{0}

and passing through

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

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

\frac{d}{d x} (cos (x^{2} + 2 x))

\frac{8 x ^{2} + 4 x + 4}{x}

x = y^{2} + 6 y, x = y

\int_{0}^{x} 4 tan (t) d t

y^{^{''}} + 9 y = e^{3 x}

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