# Homework Help: Finding rate of change formulas with the given information

1. Apr 4, 2013

### Dustobusto

1. The problem statement, all variables and given/known data

Let Q(t)=t2. Find a formula for the average rate of change (ROC) of Q over the interval [1, t] and use it to estimate the instantaneous ROC at t = 1.

2. Relevant equations

For x1 ≠ x0, the average rate of change of y with respect to x over [x0, x1] is the ratio

Average ROC = Δf/Δx = f(x1) - f(x0) / x1 - x2

Finding the instantaneous rate of change is basically the same as finding the avg ROC, except instead of using the intervals that are given (say [7, 10] for example) they give you one number, and you create your own intervals by choosing numbers extremely close to that given number (say [7, 7.01] or [7, 6.99] etc.)

3. The attempt at a solution

All I can think of is plugging in the intervals as with previous problems. Plugging t into t gives you t.

Plugging 1 into t gives you one squared which is one. Then you subtract those two to get

t2 - 1. The bottom portion which is x1 - x2 would look just like t - 1.

So maybe t squared minus one over t minus one is the formula? I suppose I could factor it out to

(t +1)(t - 1) / (t - 1) cancel out the expressions and get t + 1. So t + 1 would be the requested formula for the average rate of change? To get instantaneous ROC at t = 1, wouldn't I just plug one into "t" and get 2?

That can't be right

Last edited: Apr 4, 2013
2. Apr 4, 2013

### Dustobusto

Anyone have some ideas?

3. Apr 5, 2013

### ehild

It looks right.

ehild