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

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

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

tangent of

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

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

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}^{2} + 4)

Find the slope of

y = x^{4} - 5 x^{2} + 4 : \frac{d y}{d x} = 4 x^{3} - 10 x

Compute the slope of

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

x = a_{0} : m = 4 a_{0}^{3} - 10 a_{0}

Find the line with slope m=

4 a_{0}^{3} - 10 a_{0}

and passing through

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

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

\frac{d}{d x} (e^{s i n (2 x)} + sin (e^{2 x}))

x \to 2 lim (\frac{1}{x ( x - 2 )})

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

x \to \infty lim (\frac{2}{3})

\frac{d}{d x} (1 + x^{\frac{3}{2}})

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