So this has to be the earliest I've ever posted a blog.
At the beginning of this week we had our second calculus test. The test focused on the first derivative test, second derivative test, and how to find absolute maximums and minimums. Tuesday, we learned Extreme Value Theorem, Rolle's theorem, and Mean Value Theorem. Wednesday we started Optimization, Thursday we had a quiz on the theorems and at the end of the class through Friday we continued to learn and work problems using Optimization.
EVT:
a continuous function on a closed interval [a,b] must have both a mnimmum and a maximum on the interval; however, the maximum and minimum can occur at the endpoints.
Rolle's:
Let f be continuous on a closed interval [a,b] and differentiable on the open interval (a,b). If f(a)=f(b), then there is at least one number "c" in (a,b) such that f(c)=0.
MVT:
If f is continuous on the closed interval [a,b] and differentiable on the open interval (a,b), then there exists a number "c" in (a,b) such that f '(c)=f(b)-f(a)/b-a
Optimization is either streaching out an equation or simplifying it
The steps for optimization are:
1. Identify all given quantities and quantities to be determined. If possible, make a sketch.
2. Write a primary equation for the quantity that is to be maximized or minimized.
3. Reduce the primary equation to one having a single independent variable. This may involve the use of secondary equations relating the independent variables of the primary equation.
4. Determine the feasible domain of the primary equation. That is, determine the values for which the stated problem makes sense.
5. Determine thedesired maximum or minimum value
I understand that I have to follow these steps, but I don't know when I'm finished a step. I get confused with when to use a primary or secondary equation and how to get these equations. Can someone please explain?
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As far as your two equations, you just use
ReplyDeletesecondary, primary, then secondary.
.. the steps tell you when to switch.
determining which equation is which..
well you explained to chelsea in your comment
but the other thing which helps me to tell the difference is that the primary equation is usualy the orignal, as in the volume formula or the area formula, where as the secondary equation is usually a form of the primary, but manipulated to fit the particular dimensions/problem. Also, from what i've seen, the secondary is almost always given to you, the primary is the one you usually have to know because its usually common things such as area like i said previously.
the real difference between primary and secondary is simply that the primary equation is what value you are maximizing or minimizing. if it asks you for the maximum area of a triangle that has a perimeter of 15, the area formula for a triangle would be your primary and the perimeter formula (set equal to 15) would be your secondary.
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