(Solved): Consider the following functian. \[ y=\frac{x^{3}}{3}+\frac{x^{2}}{2}-2 x+2 \] (a) Find \( y^{\pri ...

Consider the following functian. \[ y=\frac{x^{3}}{3}+\frac{x^{2}}{2}-2 x+2 \] (a) Find \( y^{\prime}=f^{\prime}(x) \). \( f^{\prime}(x)=x^{2}+x-2 \quad \) Well done. (b) Find the critical values. (Enter your answers as a comma-separated list.) \( x= \) (c) Find the citical points. \( (x, y)=\left(\begin{array}{c}\end{array}\right)( \) smaller \( x \)-value) \( (x, y)=\left(\begin{array}{c}4\end{array}\right) \) (larger \( x \)-value) (d) Find intervals of \( x \)-values where the function is increasing-(Enter your answer using interval notation.) \( (-\infty,-2) \cup(1, \infty) \) well done! Find intervals of \( x \)-values where the function is decreasing. (Enter your answer using interval notation.) Amaxing jub. relative maxima relative minima \( (x, y)=(\quad x) \) \( (x, y)=(\quad x) \) \( (x, y)=\left(\begin{array}{ll} & x\end{array}\right) \)