For the following function:

$$\simplify{y = 2x^3-3{(x12+x22)}x^2+6{x12*x22}x+{c02}}$$

Determine the coordinates and the nature of the stationary points.

First Derivative; $y^{\prime}(x) =$ interpreted as

$\displaystyle{}$

Expected answer:interpreted as

$\displaystyle{6 x^{ 2 } + 18 x + 12}$

Give values of x where stationary points occur: smallest-$x_1$ =Write your answer as a fraction.Expected answer:,    largest-$x_2$ = Write your answer as a fraction.Expected answer:

Second Derivative is $~ y^{\prime\prime}(x) =$ interpreted as

$\displaystyle{}$

Expected answer:interpreted as

$\displaystyle{12 x + 18}$

Values of Second derivative at stationary points: 

$y^{\prime\prime}(x_1) =$interpreted as

$\displaystyle{}$

Expected answer:interpreted as

$\displaystyle{-6}$

$y^{\prime\prime}(x_2) =$interpreted as

$\displaystyle{}$

Expected answer:interpreted as

$\displaystyle{6}$

Minimum point: $\big($ interpreted as

Expected answer:interpreted as

$\displaystyle{-1}$

$,$ interpreted as

Expected answer:interpreted as

$\displaystyle{-36}$

$\big)$ and maximum point: $\big($ interpreted as

Expected answer:interpreted as

$\displaystyle{-2}$

$,$ interpreted as

Expected answer:interpreted as

$\displaystyle{-35}$

$\big)$

Enter fractions in their simplest form.