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

The tangent of x^4+5x^2-x is y=(4a_{0}^3+10a_{0}-1)x-3a_{0}^4-5a_{0}^2

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

tangent of

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

y = (4 a_{0}^{3} + 10 a_{0} - 1) x - 3 a_{0}^{4} - 5 a_{0}^{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}^{2} - a_{0})

Find the slope of

y = x^{4} + 5 x^{2} - x : \frac{d y}{d x} = 4 x^{3} + 10 x - 1

EN : T i tl e G e n er a l Eq u a t i o n Sl o p e A t P o in t 2 Eq : m = 4 a_{0}^{3} + 10 a_{0} - 1

Find the line with slope m=

4 a_{0}^{3} + 10 a_{0} - 1

and passing through

(a_{0}, a_{0}^{4} + 5 a_{0}^{2} - a_{0}) : y = (4 a_{0}^{3} + 10 a_{0} - 1) x - 3 a_{0}^{4} - 5 a_{0}^{2}

y = (4 a_{0}^{3} + 10 a_{0} - 1) x - 3 a_{0}^{4} - 5 a_{0}^{2}

h (w) = \frac{w ^{2} - 1}{w ^{2} + 1}

\frac{d}{d x} (\frac{x ^{3}}{12})

\frac{1}{2} (9 t^{2} + t)^{- 3}

\int_{0}^{1} x^{2} + x d x

y^{^{''}} + y = 0, y (0) = 0

What is the tangent of x^4+5x^2-x ?
The tangent of x^4+5x^2-x is y=(4a_{0}^3+10a_{0}-1)x-3a_{0}^4-5a_{0}^2