What is the tangent of 4x^2-2x+6 ?

The tangent of 4x^2-2x+6 is y=(8a_{0}-2)x-4a_{0}^2+6

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tangent of 4x^2-2x+6

tangent of

4 x^{2} - 2 x + 6

y = (8 a_{0} - 2) x - 4 a_{0}^{2} + 6

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, 4 a_{0}^{2} - 2 a_{0} + 6)

Find the slope of

y = 4 x^{2} - 2 x + 6 : \frac{d y}{d x} = 8 x - 2

Compute the slope of

y = 4 x^{2} - 2 x + 6

x = a_{0} : m = 8 a_{0} - 2

Find the line with slope m=

8 a_{0} - 2

and passing through

(a_{0}, 4 a_{0}^{2} - 2 a_{0} + 6) : y = (8 a_{0} - 2) x - 4 a_{0}^{2} + 6

y = (8 a_{0} - 2) x - 4 a_{0}^{2} + 6

\int \frac{2 + 3 sin ^{2} ( x )}{sin ^{2} ( x )} d x

y^{^{'}} + \frac{4}{x ^{2} - 1} y = 0

\int 4 t^{2} d t

x \to 1 lim (- \frac{1}{x - 1})

\frac{7 + t + t ^{2}}{t}

What is the tangent of 4x^2-2x+6 ?
The tangent of 4x^2-2x+6 is y=(8a_{0}-2)x-4a_{0}^2+6