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

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

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tangent of x^2+3x-1

tangent of

x^{2} + 3 x - 1

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

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)

Find the slope of

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

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

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

\int_{- 1}^{1} \frac{2}{x + 1} d x

x^{2} - 3, y = 0, - 2, 2

\int \frac{x}{( x ^{2} + 1 ) ^{\frac{7}{2}}} d x

f (x) = 5 sin (x) cos (x)

(x, y) \to (π, 3) lim (\frac{y cos ( 2 x )}{y + cos ( x )})

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