Hints for Exercise 2.1.4

Dana Ernst 12 Sep 2010 22:22

Your goal is to simplify the following expression as much as possible.

(1)\begin{align} \frac{f(1+\Delta x)-f(1)}{\Delta x} \end{align}

As with the other problems similar to this one, your general goal is to whack a factor of $\Delta x$. Here's what you should be shooting for:

(2)\begin{align} \frac{3+3\Delta x +(\Delta x)^2}{1+\Delta x} \end{align}

Lastly, you need to plug in 0 for $\Delta x$ to obtain the slope of the tangent line to $f$ at $x=1$.