In many textbooks the derivative (or IROC) is described in terms of $x$ and $∆x$ (delta $x$) instead of $x$ and $h$.

1. Explain why $h$ and $∆x$ are equivalent.

   Hint (a):

   $∆x$ can be translated as 'change in $x$.' $h$ typically appears in the expression: $(x + h)-x$. How are these equivalent?

2. Use the picture above and the definition of IROC to write the slope of the tangent line in terms of $x$ and $∆x$.

   Hint (b):

   'Definition of the Derivative' is the same thing as 'Instantaneous Rate of Change': IROC
   $f'(x)=\lim\limits_{h\rightarrow 0}\frac{f(x+h)-f(x)}{(x+h)-h}=\lim\limits_{h\rightarrow 0}\frac{f(x+h)-f(x)}{h}...$