# Word Problem ! Beginning Calculus

1. Jul 8, 2009

### I'm

1. The problem statement, all variables and given/known data[/b]
A cyclist is riding on a path modeled by f(x)= 0.08x where f and f(x) are measured in miles. Find the rate of change in elevation when x = 2

2. Relevant equations

(f(∆x + x ) - f(x))/∆x
∆x$$\stackrel{lim}{\rightarrow}$$ 0

3. The attempt at a solution

I plugged everything into the formula and got

.00008 / .0001 = .08.

I think I'm doing something wrong here.

2. Jul 8, 2009

### Дьявол

So you got
$$\lim_{\triangle x \rightarrow 0}\frac{f(\triangle x+x)+f(x)}{\triangle x}$$

$$\lim_{\triangle x \rightarrow 0}\frac{0.08(\triangle x+x) - 0.08x}{\triangle x}$$

So yes, 0.08 is the final answer.

3. Jul 8, 2009

### CompuChip

Your answer looks correct, but it appears you didn't take the limit. Instead, you just plugged in an arbitrary value for $\Delta x$. Just leave it as it is: what is $f(x + \Delta x) - f(x)$ when you plug in the definition of f?

4. Jul 8, 2009

### Staff: Mentor

Make that "where x and f(x) are measured in miles."
The answer is numerically correct, but you might need to give units, which are miles/mile. Note that the cyclist's path is a straight line whose slope can be determined merely by observation. The instantantaneous rate of change of f is going to be the same for all values of x, because the graph of f is straight line.