Question

The derivative of h(x) is given by the function h '(x) = x + 2cosx. Use your calculator to determine the number of times the graph of h(x) changes concavity on the interval [0, ]. Justify your answer using a complete sentence.

Answer 1

[0,4PI]

Answer 2

http://www.wolframalpha.com/input/?i=x+%2B+2*cosx+from+0+to+pi

Answer 3

derive it two times and do it equal zero

Answer 4

= 1 - 2sin(X)

Answer 5

dont get the second part

Answer 6

w8 nvm is it 2?

Answer 7

concavity is tested by y'' test

Answer 8

0=1-2sin(x)

-1=-2sin(x)

1/2=sin(x)

Answer 9

happens at pi/6

Answer 10

only once?

Answer 11

nope it says in the interval of 0 to 4pi

Answer 12

so two revolutions

Answer 13

ok

Answer 14

so it's pi/6, 5pi/6, 13pi/6, 17pi/6

Answer 15

using a calculator if you look at the graph

Answer 16

k thanks

Answer 17

what do you mean by 2 revolutions?

Answer 18

you'd have to integrate up one to actually see the graph of the function but the inflection points

http://www.wolframalpha.com/input/?i=x%5E2%2F2%2B+2*sinx+from+0+to+4pi

you can see at certain points it switches from concave up to concave down

Answer 19

2 revolutions around the unit circle

Answer 20

4pi =720 degrees

Answer 21

alright

Answer 22

thanks again

Answer 23

no problm