What is the tangent of-3/2 x^2+4x+4 ?

The tangent of-3/2 x^2+4x+4 is y=(-3a_{0}+4)x+3/2 a_{0}^2+4

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tangent of-3/2 x^2+4x+4

tangent of

- \frac{3}{2} x^{2} + 4 x + 4

y = (- 3 a_{0} + 4) x + \frac{3}{2} a_{0}^{2} + 4

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, - \frac{3}{2} a_{0}^{2} + 4 a_{0} + 4)

Find the slope of

y = - \frac{3}{2} x^{2} + 4 x + 4 : \frac{d y}{d x} = - 3 x + 4

Compute the slope of

y = - \frac{3}{2} x^{2} + 4 x + 4

x = a_{0} : m = - 3 a_{0} + 4

Find the line with slope m=

- 3 a_{0} + 4

and passing through

(a_{0}, - \frac{3}{2} a_{0}^{2} + 4 a_{0} + 4) : y = (- 3 a_{0} + 4) x + \frac{3}{2} a_{0}^{2} + 4

y = (- 3 a_{0} + 4) x + \frac{3}{2} a_{0}^{2} + 4

\int x^{- \frac{1}{5}} d x

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

\int x ((1 - x^{2})^{\frac{3}{2}} - x^{3}) d x

What is the tangent of-3/2 x^2+4x+4 ?
The tangent of-3/2 x^2+4x+4 is y=(-3a_{0}+4)x+3/2 a_{0}^2+4