A3.1

verify the power rule for functions of the form $f(x)=x^n$, where $n$ is a natural number [e.g., by determining the equations of the derivatives of the functions $f(x)=x$, $f(x)=x^2$, $f(x)=x^3$, and $f(x)=x^4$ algebraically using ${\lim }_{h\to 0}\frac{f(x+h)-f(x)}{h}$ and graphically using slopes of tangents]