Question

Need help! Got through finding the first derivative, but not too sure about my answer. Here is the question: When g(t) = t+ cost , -2pi less than or equal to "t" less than or equal to 2pi
A) Find the intervals of increase of decrease
B) Find the local max and mins
C) Find the intervals of concavity and inflection points
D) Use the information from parts A-C to sketch the graph.

Answer 1

So for the first derivative I got: g' (t) = 1-sint t and so the critical values would be pi/2 & -pi/2 ?

Answer 2

sin(x) = 1 when x = ...

in the interval of the function

Answer 3

when x= -pi/2 and pi/2 ?

Answer 4

just pi/2 so far

Answer 5

-pi/2 is the negative y axis and the sin would be -1

Answer 6

so you can subtract 2 pi from pi/2 and still be in the interval of the function

Answer 7

hmm... so its jut pi/2? I get really confused when they start given me intervals where there is negatives? Does -2pi mean we go around the unit circle clockwise?

Answer 8

sin(x) = 1 , when x = pi/2 + k*2pi, for any k value

Answer 9

just swinging around 360 degrees on the unit circle to the same spot with the 2pi

Answer 10

when k=-1

x = p/2 - 2 pi = -3pi/2

Answer 11

so you have two critical points inside the interval of the function....

x = pi/2 and x = -3pi/2

Answer 12

So to test out a number before -3pi/2 can I choose -pi?

Answer 13

no , larger, -3/2 is -1.5

Answer 14

try -2pi

Answer 15

That would give me a postive value when plugged in

Answer 16

right, do the same for the other 2 intervals...

Answer 17

Could I plug in 0 for the numbers between -3pi/2 and pi/2 and then 2pi after pi/2?

Answer 18

yes of course

Answer 19

sorry, just making sure

Answer 20

any number inside the interval will work ,

Answer 21

thats weird, all of them give me postive values? So does that mean that there is no interval where the function is decreasing?

Answer 22

yep, the function is always increasing over the interval, but they do have horizontal tangents at those critical values like above

Answer 23

calculate the y values, so you can add the (x,y) points for those two points on the graph

Answer 24

since it is always increasing you can sketch a rough draft , you may want to calculate the x and y intercept points also