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

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

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tangent of x^2+3x-2

tangent of

x^{2} + 3 x - 2

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

Find the slope of

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

Compute the slope of

y = x^{2} + 3 x - 2

x = a_{0} : m = 2 a_{0} + 3

Find the line with slope m=

2 a_{0} + 3

and passing through

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

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

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

- 0.1 x^{2} - x + 40

\int 7 x e^{(3 x - 1)} d x

n = 1 \sum \infty \frac{n !}{10 8 ^{n}}

y + x y^{^{'}} = a (1 + x y)

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