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

The tangent of 5x^2+5x+2 is y=(10a_{0}+5)x-5a_{0}^2+2

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tangent of 5x^2+5x+2

tangent of

5 x^{2} + 5 x + 2

y = (10 a_{0} + 5) x - 5 a_{0}^{2} + 2

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

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

Find the slope of

y = 5 x^{2} + 5 x + 2 : \frac{d y}{d x} = 10 x + 5

Compute the slope of

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

x = a_{0} : m = 10 a_{0} + 5

Find the line with slope m=

10 a_{0} + 5

and passing through

(a_{0}, 5 a_{0}^{2} + 5 a_{0} + 2) : y = (10 a_{0} + 5) x - 5 a_{0}^{2} + 2

y = (10 a_{0} + 5) x - 5 a_{0}^{2} + 2

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

y^{^{'''}} + y^{^{''}} - 2 y = 0

x \to 3 lim (\frac{4 x ^{2} - 36}{2 x - 6})

x \to 1 lim (3 x^{2} - 5 x + 4)

\int_{\frac{1}{2}}^{1} x^{- 3} - 11 d x

What is the tangent of 5x^2+5x+2 ?
The tangent of 5x^2+5x+2 is y=(10a_{0}+5)x-5a_{0}^2+2