The MAXIMUM POINT/VALUE,(dy/dx)<0,anger=95%
Okay,today i went to Yew Tee MRT Station to meet Dylan the scooby,Ying Xing and Li Ying. I was early again today. Went for sunday school and today's lesson was about''Does God Exist?''. The debate was funny and enriching as always. After sunday school,i had a great stomachache so i went to the toilet and ''make cake''. So after ''making cake'',i headed for service. As usual,i learnt alot. Then after that,i got scammed by Dylan as usual...(anger of the day=70%). Then i received a call from Ace,the HK DOG. Doggy Ace has just reached the Church compound to pick up his grand aunt. Then,i was thinking. ''I thought there were supposed to be no pets in church''. I pity his grand aunt,sure receive a fine. An old lady bringing a Dog around ''RESTRICTED PETS ZONE''. Going back to the tittle of today's post. Dylan scam+Ace,HK Dog Backstabbing=95%.I must seriously urge all my friends....STOP SCAMMING ME!!!!ENOUGH IS ENOUGH...I HAVE REACHED THE LIMIT!!!!!!!!! SERIOUSLY ENOUGH....I REALLY DON'T LIKE IT.
I will explain this theory of reaching the maximum point/value...in mathematical terms,
MAXIMUM AND MINIMUMVALUES
The turning points of a graph
WE SAY THAT A FUNCTION f(x) has a relative maximum value at x = a, if f(a) is greater than any value in its immediate neighborhood.
We call it a "relative" maximum because other values of the function may in fact be greater.
We say that a function f(x) has a relative minimum value at x = b, if f(b) is less than any value in its immediate neighborhood.
Again, other values of the function may in fact be less. With that understanding, then, we will drop the term relative.
The value of the function, the value of y, at either a maximum or a minimum is called an extreme value.
Now, what characterizes the graph at an extreme value? The tangent to the curve is horizontal. We see this at the points A and B above. The slope of each tangent line -- the derivative when evaluated at a or b -- is 0.
f '(x) = 0.
Moreover, at points immediately to the left of a maximum -- at a point C -- the slope of the tangent is positive: f '(x) > 0. While at points immediately to the right -- at a point D -- the slope is negative: f '(x) <>E and F.
We can also observe that at a maximum, at A, the graph is concave downward. (Topic 14 of Precalculus.) While at a minimum, at B, it is concave upward.
A value of x at which the function has either a maximum or a minimum is called a critical value. In the figure, the critical values are x = a and x = b.
The critical values determine turning points, at which the tangent is parallel to the x-axis. The critical values -- if any -- will be the solutions to the equation f '(x) = 0.
Example 1. Let f(x) = x² − 6x + 5.
Are there any critical values -- any turning points? If so, do they determine a maximum or a minimum? And what are the coordinates on the graph of that maximum or minimum?
Solution. f '(x) = 2x − 6 = 0 implies x = 3. (Lesson 15 of Algebra.)
x = 3 is the only critical value. It is the x-coordinate of the turning point. To determine the y-coordinate, evaluate f at that critical value -- evaluate f(3):
f(x)
=
x² − 6x + 5
f(3)
=
3² − 6· 3 + 5
=
−4.
Labels: anger management
posted by Cedric @ 3:28 PM
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