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

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

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tangent of 3x^2-5x+2

tangent of

3 x^{2} - 5 x + 2

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

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, 3 a_{0}^{2} - 5 a_{0} + 2)

Find the slope of

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

Compute the slope of

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

x = a_{0} : m = 6 a_{0} - 5

Find the line with slope m=

6 a_{0} - 5

and passing through

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

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

x \to - 9 - lim (\frac{1}{( x + 9 ) ^{2}})

\frac{d}{d x} ((9 x + 3) e^{2 x^{2} + 3})

(y - \frac{y}{x ^{2}} e^{\frac{y}{x}}) d x + (x + \frac{1}{x} e^{\frac{y}{x}}) d y = 0

\frac{d}{d x} (\frac{x ^{2} + 5 x - 1}{x ^{2}})

- 3 + 12 x - 3 x^{2}

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