Chapter 12.4, Problem 19E

(a)

To determine

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

(b)

To determine

To calculate: The points of extrema for the provided function $k\left(x\right)=\frac{2x}{3}+{\left(x+1\right)}^{2/3}$.

(c)

To determine

To calculate: The points of inflection for the provided function $k\left(x\right)=\frac{2x}{3}+{\left(x+1\right)}^{2/3}$.

(d)

To determine

The behavior near singular points of the function $k\left(x\right)=\frac{2x}{3}+{\left(x+1\right)}^{2/3}$.

(e)

To determine

The behavior at infinity for the provided function $k\left(x\right)=\frac{2x}{3}+{\left(x+1\right)}^{2/3}$.