Question

What is the rate of change from

Answer 1

x = 0 to x = \[\frac{ \pi }{ 2 }\]

Answer 2

@phi

Answer 3

figure out change in y divided by change in x

Answer 4

\[-\frac{ \pi }{ 6 }\]
\[-\frac{ 6 }{ \pi } \]
\[\frac{ \pi }{ 6 }\]
\[\frac{ 6 }{ \pi }\]

Answer 5

so (0,0) to (1,0)? I get confused on these too

Answer 6

we start at (0,0) and stop at x= pi/2
what is the y value at x= pi/2 ?

Answer 7

put you finger on pi/2 on the x-axis, move up until you hit the red curve

Answer 8

3

Answer 9

I thought you had bad eyes. yes, we "stop at y=3"
we started at (0,0) i.e. at x=0, y is 0
what is the change in y ?
what is final y - first y ?

Answer 10

then figure out change in x
last x - first x

Answer 11

no i was just typing too fast haha
change in y = 3
change in x = 0

Answer 12

ok on y
the change in x is the last x minus the first x over our interval.
the first x is 0. what is the last x we use ?

Answer 13

pi/2

Answer 14

and the change in x is pi/2 - 0 or just pi/2

Answer 15

now we write the fraction: change in y divided by change in x
\[ \frac{3}{ \frac{\pi}{2}} \]

Answer 16

to simplify that I would multiply top and bottom by 2/pi

Answer 17

6/pi

Answer 18

\[ \frac{3\cdot \frac{2}{\pi}}{ \frac{\pi}{2}\cdot \frac{2}{\pi}} \]

Answer 19

yes, the average change in y over change in x is about 1.9

Answer 20

ok all of this makes sense now, whenever i saw problems like this i would draw a blank

Answer 21

thanks foe the help, much appreciated!

Answer 22

for

Answer 23

yw