Chapter 5.4, Problem 11E

(a)

To determine

To calculate: The $x$ and $y$ intercepts of the provided function $g\left(t\right)=\frac{1}{4}{t}^4-\frac{2}{3}{t}^3+\frac{1}{2}{t}^2$.

(b)

To determine

To calculate: The points of extrema for the provided function $g\left(t\right)=\frac{1}{4}{t}^4-\frac{2}{3}{t}^3+\frac{1}{2}{t}^2$.

(c)

To determine

To calculate: The points of inflection for the provided function $g\left(t\right)=\frac{1}{4}{t}^4-\frac{2}{3}{t}^3+\frac{1}{2}{t}^2$.

(d)

To determine

The behavior near singular points of the function $g\left(t\right)=\frac{1}{4}{t}^4-\frac{2}{3}{t}^3+\frac{1}{2}{t}^2$.

(e)

To determine

The behavior at infinity for the provided function $g\left(t\right)=\frac{1}{4}{t}^4-\frac{2}{3}{t}^3+\frac{1}{2}{t}^2$.