# Sketching the Curves of a Function W/In an Interval - Simple (1st Year Calcu

• washablemarker
In summary, the conversation was about sketching the graph of a function on the interval [0, 2pi]. The poster had some difficulties locating all of the relative extreme values and asked for help. They eventually realized their mistake of not using the double angle trig formula and marked the post as solved.
washablemarker
[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)

## 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:

1. domain and range
2. x and y intercepts
3. whether or not there is discontinuity
4. whether or not there is symmetry
5. intervals of increasing and decreasing order
6. extrema
7. points of inflection
8. concavity
9. 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?

Last edited by a moderator:
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.

How did you solve this equation?

ah. figured it out. i had worked out the values mentally real quick and hadn't realized that i needed to use the double angle trig formula. sheesh. yet another simple algebra mistake. is there a way i could mark this for deletion or something? by the way, thank you. sometimes it can be difficult to see a mistake of your own you know.

You are welcome!

Just edit the title and marked it [SOLVED]

## 1. What is sketching the curves of a function in an interval?

Sketching the curves of a function within an interval is the process of visually representing the behavior of a function over a specific range of inputs. This involves plotting points on a graph and connecting them to create a curve that represents the shape of the function within the given interval.

## 2. Why is it important to sketch the curves of a function?

Sketching the curves of a function is important because it allows us to gain a better understanding of the behavior of the function. It can help us identify key features such as the domain and range, intercepts, and critical points. It also allows us to make predictions about the behavior of the function outside of the given interval.

## 3. What information do I need to sketch the curves of a function?

To sketch the curves of a function within an interval, you will need the function itself as well as the interval over which you want to graph it. It can also be helpful to have a basic understanding of the behavior of different types of functions, such as linear, quadratic, and exponential functions.

## 4. What are some key steps to follow when sketching the curves of a function?

The key steps to follow when sketching the curves of a function include identifying the domain and range, finding and plotting key points such as intercepts and critical points, determining the end behavior, and connecting the points to create a smooth curve. It can also be helpful to label the axes and add a title to the graph.

## 5. Are there any common mistakes to avoid when sketching the curves of a function?

Some common mistakes to avoid when sketching the curves of a function include not identifying the correct domain and range, not plotting enough key points to accurately represent the function's behavior, and not connecting the points with a smooth curve. It's also important to carefully label the axes and title the graph to clearly communicate the information being represented.

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