Chapter 2.2, Problem 69E

(a)

To determine

To graph: The functions $f\left(x\right)=x^3$ and $g\left(x\right)=x^3+3$ by use of graphing utility.

(b)

To determine

To calculate: The value of $f^{\prime }\left(1\right)\text{ and }{g}^{\prime }\left(1\right)$ for the functions $f\left(x\right)=x^3$ and $g\left(x\right)=x^3+3$.

(c)

To determine

To graph: The tangent line to the graph of the functions $f\left(x\right)=x^3$ and $g\left(x\right)=x^3+3$ at $x=1$.

(d)

To determine

The relationship between $f^{\prime }\left(x\right)=3x^2$ and $g^{\prime }\left(x\right)=3x^2$.