# Thread: [SOLVED] Rates of change formula?

1. ## [SOLVED] Rates of change formula?

I'm trying to solve the question for f(x)= x + sin x find the average rate of change of f(x) for

i) [0, pi / 2]

I think the formula is f(b)-f(a) / b-a

in which this case we would have

pi/2 + sin pi/2 - sin0 / pi/2 - 0

I'm not sure if I got this right though.

Edit: Okay so I got my formula:

change over y / change over x

f(x2) - f(x1) / fx2 - fx1

In the above scenario I think we have to factor out something to eliminate the denominator but I'm not sure how to do it.

2. Simplify $\displaystyle \frac{\frac{\pi}{2} + \sin \left(\frac{\pi}{2}\right)}{\frac{\pi}{2}}$

3. Originally Posted by thekrown
I think the formula is f(b)-f(a) / b-a
correct $\displaystyle \frac{f(b)-f(a)}{ b-a}$

4. Okay so I can factor out pi/2 and end up with

pi/2 (sin 1) / pi/2

I can then cross out pi/2 from the numerator and denominator. This leaves us with sin 1.

I remember some problems where I would turn to the unit circle, find the location and then find sin by finding y/r or something similar.

However, in this case I don't really know what sin 1 is since usually there is a pi somewhere.

5. Originally Posted by thekrown
Okay so I can factor out pi/2 and end up with

pi/2 (sin 1) / pi/2

I can then cross out pi/2 from the numerator and denominator. This leaves us with sin 1.
That is all wrong.

$\displaystyle \sin \left(\frac{\pi}{2}\right)=1$

6. I see, so in this case we have pi/2 + 1/2 divided by pi/2

I think this is equal to 2pi/2 divided by pi/2 which should be 2 right?

7. $\displaystyle \frac{\frac{\pi}{2} + \sin \left(\frac{\pi}{2}\right)}{\frac{\pi}{2}}= \frac{\frac{\pi}{2} + 1}{\frac{\pi}{2}} = \frac{2}{\pi}\left(\frac{\pi}{2} + 1\right) = 1+\frac{2}{\pi}$

8. Originally Posted by thekrown
I see, so in this case we have pi/2 + 1/2 divided by pi/2

I think this is equal to 2pi/2 divided by pi/2 which should be 2 right?
(pi/2 + 1/2) divided by pi/2 = (pi/2 + 1/2) times 2/pi