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

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

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tangent of-5/2 x^2+2x+2

tangent of

- \frac{5}{2} x^{2} + 2 x + 2

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

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, - \frac{5}{2} a_{0}^{2} + 2 a_{0} + 2)

Find the slope of

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

Compute the slope of

y = - \frac{5}{2} x^{2} + 2 x + 2

x = a_{0} : m = - 5 a_{0} + 2

Find the line with slope m=

- 5 a_{0} + 2

and passing through

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

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

\int 3 x^{2} y^{2} d x

\int_{3}^{5} (x^{4} - \frac{3}{x ^{3}}) d x

2 (ln (y)) y^{^{'}} - x^{5} y = 0

y = cos (a^{5} + x^{5})

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

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