8th post

this week was about reviewing and doing a billion packets.......

review:

The derivative:
of a function at a chosen input value describes the best linear approximation of the function near that input value. For a real-valued function of a single real variable, the derivative at a point equals the slope of the tangent line to the graph of the function at that point.

optimazation:
In the simplest case, this means solving problems in which one seeks to minimize or maximize a real function by systematically choosing the values of real or integer variables from within an allowed set. This formulation, using a scalar, real-valued objective function, is probably the simplest example; the generalization of optimization theory and techniques to other formulations comprises a large area of applied mathematics. More generally, it means finding "best available" values of some objective function given a defined domain, including a variety of different types of objective functions and different types of domains.

Rolle's theorem:
essentially states that a differentiable and continuous function, which attains equal values at two points, must have a point somewhere between them where the slope of the tangent line to the graph of the function is zero.

the mean value theorem:
states, roughly, that given a section of a smooth (differentiable) curve, there is at least one point on that section at which the derivative (slope) of the curve is equal (parallel) to the "average" derivative of the section.[1] It is used to prove theorems that make global conclusions about a function on an interval starting from local hypotheses about derivatives at points of the interval.


okay so im still having problems with optimazation so if anyone can put examples up that would be helpful.