What is the tangent of 3x^2-14x+5 ?

The tangent of 3x^2-14x+5 is y=(6a_{0}-14)x-3a_{0}^2+5

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tangent of 3x^2-14x+5

tangent of

3 x^{2} - 14 x + 5

y = (6 a_{0} - 14) 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} - 14 a_{0} + 5)

Find the slope of

y = 3 x^{2} - 14 x + 5 : \frac{d y}{d x} = 6 x - 14

Compute the slope of

y = 3 x^{2} - 14 x + 5

x = a_{0} : m = 6 a_{0} - 14

Find the line with slope m=

6 a_{0} - 14

and passing through

(a_{0}, 3 a_{0}^{2} - 14 a_{0} + 5) : y = (6 a_{0} - 14) x - 3 a_{0}^{2} + 5

y = (6 a_{0} - 14) x - 3 a_{0}^{2} + 5

\frac{9}{x ^{2} + 2}

\int_{0}^{4} \frac{x}{x ^{2} + 9} d x

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

x \to + 0 lim (ln (x^{2}))

\frac{2 s + 1}{2 s ^{2} + s + 1}

What is the tangent of 3x^2-14x+5 ?
The tangent of 3x^2-14x+5 is y=(6a_{0}-14)x-3a_{0}^2+5