Post 23...blogger fails..miserably

I am having major problems with this blogger thing. KEEPS KICKING ME OFF!!!!!!

Ok...Math!!!!!

To begin with, there are certain steps by which you must follow in order to attain the absolute maximum and minimum of a graph.

1. Find critical values by using the first derivative test: take the derivative set equal to zero and solve for the variable.

2. Plug both intervals as well as the critical values into your original equation

3. Be sure to keep the value after substitution with each appropriate number.

4. To determine which constitute a max and which constitute a min, you must look and point out those of which have the lowest values-min- and those of the highest value-max.

In an effort to further explain the above, I will now complete an example problem similar to that on an AP exam which we take later in the year.

Example:

Given the original function f(x) = x^2 -16 on the interval [1,2], find any absolute maxima and minima.

1. First Derivative Test:
f’(x) = 2x
2x = 0
X = 0 <<
2/3. (0)^2 + 16= 16>>[0,,16]
(1)^2 + 16= 17>>[1, 17]
(2)^2 + 16= 20>>[2, 20]

4. In accordance with the above data, as well as the aforementioned steps, one can infer that there is an absolute minimum at [1, 16] and an absolute maximum at [2, 20].

Hopefully the above explanation has clarified a few things and/or helped you in some shape or form.

In yet another effort to clarify a specific topic or idea in Calculus, I shall further explain the concept from blogs one and two.

While all of the information in the previous reflections were indeed correct, after supplementary review, I have found that I could have given an example seen on some free response questions on the AP.

For example, they may ask you if a certain type of sum, such as LRAM, is an overestimate or an underestimate. My method to finding the answer to this question is relatively simple, however, it requires a substantial understanding of derivative graphs.

But in simple terms:
IF:
f’(x) > 0--increasing
f’’(x) <0--concave down

THEN:
LRAM-underestimate
RRAM-overestimate
MRAM-overestimate
TRAM-underestimate (barely-closest estimate)

IF:
f’(x) <0--decreasing
f’’(x).0--concave up

THEN:
LRAM-overestimate
RRAM-underestimate
TRAM-overestimate
MRAM-investigate

Hope that helps some!
**This comes in handy on the problems that have "T