Chapter 12.2, Problem 20E

(a)

To determine

To calculate: The derivative $r\text{'}\left(t\right)$ for the provided function $r\left(t\right)=\left(t^2+t\right)i+\left(t^2-t\right)j$.

(b)

To determine

To calculate: The Second derivative $r\text{'}\text{'}\left(t\right)$ for the provided function $r\left(t\right)=\left(t^2+t\right)i+\left(t^2-t\right)j$.

(c)

To determine

To calculate: The dot product $r\text{'}\left(t\right)\cdot r\text{'}\text{'}\left(t\right)$ for the provided function $r\left(t\right)=\left(t^2+t\right)i+\left(t^2-t\right)j$.