What is the tangent of x^4+9x^2-x(1.9) ?

The tangent of x^4+9x^2-x(1.9) is y=(4a_{0}^3+18a_{0}-1.9)x-3a_{0}^4-9a_{0}^2

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tangent of x^4+9x^2-x(1.9)

tangent of

x^{4} + 9 x^{2} - x (1.9)

y = (4 a_{0}^{3} + 18 a_{0} - 1.9) x - 3 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}, a_{0}^{4} + 9 a_{0}^{2} - a_{0} \cdot 1.9)

Find the slope of

y = x^{4} + 9 x^{2} - x 1.9 : \frac{d y}{d x} = 4 x^{3} + 18 x - 1.9

Compute the slope of

y = x^{4} + 9 x^{2} - x 1.9

x = a_{0} : m = 4 a_{0}^{3} + 18 a_{0} - 1.9

Find the line with slope m=

4 a_{0}^{3} + 18 a_{0} - 1.9

and passing through

(a_{0}, a_{0}^{4} + 9 a_{0}^{2} - a_{0} 1.9) : y = (4 a_{0}^{3} + 18 a_{0} - 1.9) x - 3 a_{0}^{4} - 9 a_{0}^{2}

y = (4 a_{0}^{3} + 18 a_{0} - 1.9) x - 3 a_{0}^{4} - 9 a_{0}^{2}

f (x) = x^{2} + 2, at x = - 1

\frac{d}{d t} (\frac{1}{1 + 4 t ^{2}})

\frac{\partial}{\partial x} (\frac{x e ^{y}}{x + y})

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

\int \frac{x + 6}{( x + 2 ) ^{2}} d x

What is the tangent of x^4+9x^2-x(1.9) ?
The tangent of x^4+9x^2-x(1.9) is y=(4a_{0}^3+18a_{0}-1.9)x-3a_{0}^4-9a_{0}^2