Question

Contsruct a graph after finding the following:
A:Domain
B:X and Y intercepts
C:Symetry
D:Asymptotes
E:Interval of Increase/Decrease
F:Local Max/Min
G:Curvature and Inflection points

Answer 1

\[y=\sin^3x\]

Answer 2

Domain is all real numbers.

Answer 3

x intercept =

Answer 4

\[0=\sin^3x\]

Answer 5

\[\pi(n)\]

Answer 6

y intercept = 0

Answer 7

symetry = odd about the orgin

Answer 8

no asymptotes

Answer 9

\[f'(x)=3\sin^2xcosx\]

Answer 10

\[3\sin^2x=0\]

Answer 11

\[cosx=0\]

Answer 12

so my critical points for intervals of increase and decrease are

Answer 13

\[\pi/2,-\pi/2\]

Answer 14

Where are those 2 values coming from? From the cosine part?

Answer 15

the cosx=0 at pi/2

Answer 16

then the 3sin^2x=0, = 1-cosx/2=0 = cos2x=1

Answer 17

shoot now im not sure, somehow the book has the interval of 0<x<pi

Answer 18

\[cosx=0 \rightarrow x=\frac{ \pi }{ 2 }\pm \pi (n)\]
Hmm your first set of critical points looks good.
I think the next one you want to simply solve like this.
\[3\sin^2x=0\] Dividing both sides by 3, then taking the square root of both sides, to get to this:
\[sinx=0\rightarrow x=0 \pm \pi(n)\]

Answer 19

ok, so my intervals are inc(0,pi/2) dec(pi/2,pi)

Answer 20

my local max is f(pi/2) = 1

Answer 21

ok so for second derivative, is it safe to say that 3sin^2x is f and cosx is g? (using the product rule)

Answer 22

mhm that seems fine c: