0

Find the average rate of change for the following functions please. I'm facing problems in these.

  1. $s=2t^3-5t+7$ interval from $t=1$ to $t=3$
  2. $h=\sqrt{2t}-7$ interval from $t=8$ to $t=8.5$
Mathmo123
  • 23,018
Ahmad
  • 19
  • 5
  • I solved it using the formula "delta y/delta x=(f(x+delta x)-f(x))/delta x" and the answer came 21 and 2 respectively but my book answer is 17 and .25 for each. – Ahmad Jun 24 '14 at 18:04
  • It looks like your first answer is correct. Unless there's a typo in the formula, the book seems to be wrong. For your second answer, the book is correct. Did you forget to take the square-root in your calculation? – user3294068 Jun 24 '14 at 18:53
  • yes my mistake, apart from sqr. thanks – Ahmad Jun 24 '14 at 18:57

1 Answers1

1

When I want to find the average of five numbers, I take their sum and divide it by five. It looks like this: $$\frac{x_1 + x_2 + x_3 + x_4 + x_5}{5}.$$ You've been asked to find the average value of a function, the rates of change or derivatives of $s$ and $h$.

Note that the values of a function are also a set of points, though in your case there are categorically more than five of them. Can you think of a way to do something like adding all of the values of the derivative between those bounds and then dividing by the size of the set of values?

Edit: You've been given two functions defined for $t$ in the real numbers. You can think of $t$ like time, which is to say not discrete. In your comment, you refer to the only value of $t$ between $1$ and $3$ as being $2$, though there are many more. Take $2.5$ and $1.3$ for example.

The rates of change of $s(t)$ and $h(t)$ are given by their derivatives. Can you calculate those? Then, to get the average value you have to add, which is to say integrate these functions between the given bounds and then divide by the length of the interval $3-1 = 2$.

The comment below gives a simpler and better answer than mine, though the two are equivalent.

MRicci
  • 1,646
  • I didn't understand. i'm totally new to derivatives. Are you talking about the values between the interval "t=1 to t=3"? there is just one value between them "2" – Ahmad Jun 24 '14 at 18:14
  • I've addressed your comment in an edit to my answer. – MRicci Jun 24 '14 at 18:20
  • The average rate of change of a function does not involve derivatives. The average rate of change of $f$ on the interval $[a,b]$ is simply $\frac{f(b) - f(a)}{b-a}$. – Viktor Vaughn Jun 24 '14 at 18:22
  • Oops! Got ahead of myself. Thanks for catching that. Though, if you notice, our answers our the same... – MRicci Jun 24 '14 at 18:27
  • show me the exact average change in it please? – Ahmad Jun 24 '14 at 18:29