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washablemarker

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**[SOLVED] Sketching the Curves of a Function W/In an Interval - Simple (1st Year Calcu**

## Homework Statement

Sketch the graph of the function on the interval [0, 2pi].

y = cosx - 1/2(cos2x)

## Homework Equations

## The Attempt at a Solution

so the problems that i have been practicing like this have been pretty simple. i determine all of the following:

- domain and range
- x and y intercepts
- whether or not there is discontinuity
- whether or not there is symmetry
- intervals of increasing and decreasing order
- extrema
- points of inflection
- concavity
- whether or not there exist asymptotes

the problem is that mathematically i located a single extreme value at (pi, -3/2), but graphically, there appears to be more.

http://img149.imageshack.us/img149/1645/graphscreenshotth2.th.png

is not each change in direction a relative minimum/maximum value? i can only seem to locate the absolute minimum value within the interval, but none of the other relative extreme values. any idea as to where i am going wrong?

so, the first derivative of the given function is -sinx + sin2x. solving this equation is where i find possible extrema at 0, pi, and 2pi. any ideas why i can't seem to locate the other extrema algebraically?

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