What is the tangent of y=2x^2+6x+5 ?

The tangent of y=2x^2+6x+5 is y=(4a_{0}+6)x-2a_{0}^2+5

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tangent of y=2x^2+6x+5

tangent of

y = 2 x^{2} + 6 x + 5

y = (4 a_{0} + 6) x - 2 a_{0}^{2} + 5

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, 2 a_{0}^{2} + 6 a_{0} + 5)

Find the slope of

y = 2 x^{2} + 6 x + 5 : \frac{d y}{d x} = 4 x + 6

Compute the slope of

y = 2 x^{2} + 6 x + 5

x = a_{0} : m = 4 a_{0} + 6

Find the line with slope m=

4 a_{0} + 6

and passing through

(a_{0}, 2 a_{0}^{2} + 6 a_{0} + 5) : y = (4 a_{0} + 6) x - 2 a_{0}^{2} + 5

y = (4 a_{0} + 6) x - 2 a_{0}^{2} + 5

x \to - 1 lim (\frac{2}{x ^{3} - 1})

\int_{1}^{3} x 4^{x^{2}} d x

\int \frac{1 - x ^{2}}{x ^{4}} arcsin (x) d x

\frac{\partial}{\partial t} (sin (2 t))

\frac{d ^{3} y}{d x ^{3}} + \frac{d ^{2} y}{d x ^{2}} - 2 y = 0

What is the tangent of y=2x^2+6x+5 ?
The tangent of y=2x^2+6x+5 is y=(4a_{0}+6)x-2a_{0}^2+5