What is the tangent of 2x^4-9x^2 ?

The tangent of 2x^4-9x^2 is y=(8a_{0}^3-18a_{0})x-6a_{0}^4+9a_{0}^2

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tangent of 2x^4-9x^2

tangent of

2 x^{4} - 9 x^{2}

y = (8 a_{0}^{3} - 18 a_{0}) x - 6 a_{0}^{4} + 9 a_{0}^{2}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, 2 a_{0}^{4} - 9 a_{0}^{2})

Find the slope of

y = 2 x^{4} - 9 x^{2} : \frac{d y}{d x} = 8 x^{3} - 18 x

Compute the slope of

y = 2 x^{4} - 9 x^{2}

x = a_{0} : m = 8 a_{0}^{3} - 18 a_{0}

Find the line with slope m=

8 a_{0}^{3} - 18 a_{0}

and passing through

(a_{0}, 2 a_{0}^{4} - 9 a_{0}^{2}) : y = (8 a_{0}^{3} - 18 a_{0}) x - 6 a_{0}^{4} + 9 a_{0}^{2}

y = (8 a_{0}^{3} - 18 a_{0}) x - 6 a_{0}^{4} + 9 a_{0}^{2}

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

t y^{^{'}} + (t + 1) y = t, y (ln (3)) = 1

x \to 0 lim (x^{4} (cos (\frac{2}{x})))

\int \frac{4}{5} d x

f (x) = 4^{\frac{c}{x}}

What is the tangent of 2x^4-9x^2 ?
The tangent of 2x^4-9x^2 is y=(8a_{0}^3-18a_{0})x-6a_{0}^4+9a_{0}^2