Question

Use the graph below to answer the question that follows.

Answer 1

What is the rate of change between the interval x = π and x = three pi over two?

Answer 2

rate of change
\(\Large \dfrac{f(b)-f(a)}{b-a} \)

Answer 3

\(\Large \dfrac{f(3\pi/2)-f(\pi)}{3\pi/2-\pi} \)

can you find numerator ?

Answer 4

from the graph, find
f(3pi/2) = .... ?
f(pi) = ...?

can u find ?

Answer 5

Would that be f(4.71)?

Answer 6

there's a 3pi/2 on x axis in your graph.
do you see it ?

Answer 7

\(3 \pi/2 \)

Answer 8

I multiplied 3 by 3.14 and then divided by 2 to get 4.71

Answer 9

"use the graph"

have a look at the graph! do you see "\(3\pi/2\)" on x axis ?

Answer 10

Oh I see it now; so because the dot goes up to 2, is that what we use?

Answer 11

yes!
thats the value of f(x) when x = 3pi/2
so
f(3pi/2) = 2

similarly, can you find f(pi) = ... ?

Answer 12

Okay, would f(pi) be 3.14?

Answer 13

no.....pi = 3.14

search for \(\pi\) on you x axis in the graph!

Answer 14

when x = pi
the point on the curve is at y = -1
right ???

Answer 15

so f(pi) = -1

Answer 16

Yes, sorry, it's at -1. What is the next step?

Answer 17

so your rate of change is
\(\Large \dfrac{f(3\pi/2)-f(\pi)}{3\pi/2-\pi}=\Large \dfrac{2-(-1)}{3\pi/2-\pi}\)

Answer 18

simplify that ^

Answer 19

The numerator is 3. Is -1 substituted for pi in the denominator?

Answer 20

no, pi is pi only, in denominator

Answer 21

Ok, so 3pi/2 is 2 (from the graph), and I'm not sure then how to subtract pi from that...?

Answer 22

factor out pi