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

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

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tangent of 3x^2+2x

tangent of

3 x^{2} + 2 x

y = (6 a_{0} + 2) x - 3 a_{0}^{2}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, 3 a_{0}^{2} + 2 a_{0})

Find the slope of

y = 3 x^{2} + 2 x : \frac{d y}{d x} = 6 x + 2

Compute the slope of

y = 3 x^{2} + 2 x

x = a_{0} : m = 6 a_{0} + 2

Find the line with slope m=

6 a_{0} + 2

and passing through

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

y = (6 a_{0} + 2) x - 3 a_{0}^{2}

x^{2} - 4, 5

\int_{1}^{2} x^{3} + \frac{1}{4 x ^{3}} d x

x \to \infty lim (- 7)

cos (x) - tan (x)

\frac{d y}{d x} = - y^{2}

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