What is the tangent of (x^2+3x-1)(2-x) ?

The tangent of (x^2+3x-1)(2-x) is y=(-3a_{0}^2-2a_{0}+7)x+2a_{0}^3+a_{0}^2-2

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tangent of (x^2+3x-1)(2-x)

tangent of

(x^{2} + 3 x - 1) (2 - x)

y = (- 3 a_{0}^{2} - 2 a_{0} + 7) x + 2 a_{0}^{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}^{2} + 3 a_{0} - 1) (2 - a_{0}))

Find the slope of

y = (x^{2} + 3 x - 1) (2 - x) : \frac{d y}{d x} = - 3 x^{2} - 2 x + 7

Compute the slope of

y = (x^{2} + 3 x - 1) (2 - x)

x = a_{0} : m = - 3 a_{0}^{2} - 2 a_{0} + 7

Find the line with slope m=

- 3 a_{0}^{2} - 2 a_{0} + 7

and passing through

(a_{0}, (a_{0}^{2} + 3 a_{0} - 1) (2 - a_{0})) : y = (- 3 a_{0}^{2} - 2 a_{0} + 7) x + 2 a_{0}^{3} + a_{0}^{2} - 2

y = (- 3 a_{0}^{2} - 2 a_{0} + 7) x + 2 a_{0}^{3} + a_{0}^{2} - 2

\frac{\partial}{\partial x} (1 - x)

\frac{\partial}{\partial x} (\frac{x}{x ^{2} - y ^{2}})

\int \frac{288}{( 2 x - 4 ) ^{2}} d x

f (x) = 6 x - 12, [1, 5]

x \to \infty lim (sin (x))

What is the tangent of (x^2+3x-1)(2-x) ?
The tangent of (x^2+3x-1)(2-x) is y=(-3a_{0}^2-2a_{0}+7)x+2a_{0}^3+a_{0}^2-2