After you have drawn your graph, press [2nd][TRACE] to access the (CALC) menu
In the above screen (on your calculator) press [3:minimum]
You will be promped for the lower bound of the domain where you think the minimum liesI DO NOT KNOW HOW TO FIND THE MINIMUM ON A GRAPH - 5d2b86d.jpg src="/uploads/images/5d2b86d.jpg" alt="5d2b86d.jpg" class="h_mi" />
Notice the dark spot on the curve near the X axis: That is what the calculator suggests as a lower bound. Since it is rather close to the minimum you are well advised to select this as a lower bound. To accept it press [ENTER].
You are then prompted for the right bound. Be ready to move the cursor to the right side of the minimum. That is what I had to do to get the folI DO NOT KNOW HOW TO FIND THE MINIMUM ON A GRAPH - 4263d02.jpgen. Notice the mark on the curve at X=4.7
Press [ENTER] to accept or type in a reasonable value.
The calculator prompI DO NOT KNOW HOW TO FIND THE MINIMUM ON A GRAPH - a07ff44.jpga guess. Enter a value that lies in the interval [left bound, right bound] and presI DO NOT KNOW HOW TO FIND THE MINIMUM ON A GRAPH - 94af57a.jpgr />
As you can see, I entered value X=3 and pressed [ENTER]
Here is the result. Enjoy
If you have to look for a maximum, the procedure is the same, except that at the begining of the search you select [4:maximum] on the first screen capture (see above.)
OOPS: The sentence
"Notice the dark spot on the curve near the X axis"
should read
"Notice the dark spot on the curve near the Y axis"
There is no such thing as an exact result with a calculator. Every thing is approximate. This is the way to do it. Read your calculator manual.
I took the example of a function that has a minimum to show you how to do it. I figuratively took you by the hand. All you have to do is enter your function. I SHOWED you every single step, leaving nothing out. I even went out of my way, on my own time at no cost to you, to do the screen captures from my calculator, tansfer them to my computer and insert them in the post, in the hope that it will help you and any reasonably intelligent person who can read and imitate what is shown.
If you are unable to benefit from these overly detailled explanations, then my friend, you are in serious trouble with your mathematics, and you should hire a tutor.
I do not know whether I should tell you that, but if you want to obtain the exact result, here is how it is done (with pen and paper). If you take college calculus you will learn it.
Lets us see how you fare with this. Calculate the first derivative of your function
Find the points (x-values) where that first derivative vanishes (has value 0). That entails solving by hand a (generally) non-linear equation.
Calculate the second derivative of your original function.
At the points where the first derivative vanishes (at the x-values calculated in point 2) evaluate the second derivative: replace the x-values in the expression for the 2nd derivative.
If the 2nd derivative is positive, then the original function has a minimum.
If the 2nd derivative is negative, then the oroginal function has a maximum.
If you do not understand ask for explanations.
I forgot to tell you: On the web, if you use capital letters you are signifying that you are SHOUTING.
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3. Supply the right limit of x (to the right of the minimum). Press [ENTER]
3. Supply an estimate of the X-value of the minimum.
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THIS WAY DOES NOT GIVE YOU THE EXACT ANSWER IT IS OFF
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