What is the tangent of 3x^2-2x+5 ?

The tangent of 3x^2-2x+5 is y=(6a_{0}-2)x-3a_{0}^2+5

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tangent of 3x^2-2x+5

tangent of

3 x^{2} - 2 x + 5

y = (6 a_{0} - 2) x - 3 a_{0}^{2} + 5

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} + 5)

Find the slope of

y = 3 x^{2} - 2 x + 5 : \frac{d y}{d x} = 6 x - 2

Compute the slope of

y = 3 x^{2} - 2 x + 5

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} + 5) : y = (6 a_{0} - 2) x - 3 a_{0}^{2} + 5

y = (6 a_{0} - 2) x - 3 a_{0}^{2} + 5

\frac{d y}{d x} = 8 x y

x \to 0 lim (\frac{arcsin ( 3 x )}{arctan ( 5 x )})

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

\frac{d}{d x} (x e^{x})

\frac{d}{d x} (cos (4 x) - sin (x))

What is the tangent of 3x^2-2x+5 ?
The tangent of 3x^2-2x+5 is y=(6a_{0}-2)x-3a_{0}^2+5