What is the tangent of (8x^2+4x+4)/(sqrt(4)) ?

The tangent of (8x^2+4x+4)/(sqrt(4)) is y=2(4a_{0}+1)x-4a_{0}^2+2

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tangent of (8x^2+4x+4)/(sqrt(4))

tangent of

\frac{8 x ^{2} + 4 x + 4}{4}

y = 2 (4 a_{0} + 1) x - 4 a_{0}^{2} + 2

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, 2 (2 a_{0}^{2} + a_{0} + 1))

Find the slope of

y = \frac{8 x ^{2} + 4 x + 4}{4} : \frac{d y}{d x} = 2 (4 x + 1)

Compute the slope of

y = \frac{8 x ^{2} + 4 x + 4}{4}

x = a_{0} : m = 2 (4 a_{0} + 1)

Find the line with slope m=

2 (4 a_{0} + 1)

and passing through

(a_{0}, 2 (2 a_{0}^{2} + a_{0} + 1)) : y = 2 (4 a_{0} + 1) x - 4 a_{0}^{2} + 2

y = 2 (4 a_{0} + 1) x - 4 a_{0}^{2} + 2

\int (e^{x} + 5) d x

x \to 3 lim (9 - x^{2})

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

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

\int (6 x^{2} - 5 x - 1) d x

What is the tangent of (8x^2+4x+4)/(sqrt(4)) ?
The tangent of (8x^2+4x+4)/(sqrt(4)) is y=2(4a_{0}+1)x-4a_{0}^2+2