2.1.5

2.1.5

TylerQ 13 Sep 2010 21:55

How would I go about doing the last part of problem 5? I got the a b and c parts fine enough but the last part seems a bit confusing. Thanks

Re: 2.1.5

Dana Ernst 13 Sep 2010 23:33

The last part of Exercise 2.1.5 is nearly identical to the last part of Exercise 2.1.3 and to Exercise 2.1.4. When you are asked to "use algebra to find a simple formula for the slope of the chord between 1 and $1+\Delta x$", what you need to do is simplify

(1)

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

where $f(x)=x^3$. As with the other problems, do some algebraic yoga until you can whack the $\Delta x$ in the denominator. After you've done this, all you need to do is plug in 0 for $\Delta x$, which yields the slope of the tangent line.