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Finding Absolute Extrema :Now it's time to see our first major application of derivatives. Specified a continuous function, f(x), on an interval [a,b] we desire to find out the absolute extrema of the function. To do this we will requierd many of the ideas which we looked at in the previous section.
Firstly, as we have an interval and we are considering that the function is continuous the Extreme Value Theorem described that we can actually do this. it is a good thing of course. We don't desire to be trying to determine something that may not exist.
Next, we illustrated in the earlier section that absolute extrema can take place at endpoints or at relative extrema. Also, from Fermat's Theorem we know that the list of critical points is also a list of all probable relative extrema. Thus the endpoints along with the list of all critical points will actually be a list of all probable absolute extrema.
Now we just required to recall that the absolute extrema are nothing more than the largest & smallest values which a function will take thus all that we actually required to do is get a list of possible absolute extrema, plug these points into our function and then recognize the largest & smallest values.
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If we "break up" the root into the total of two pieces clearly we get different answers. Simplified radical form: We will simplify radicals shortly so we have to next
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what is the LCM of 18, 56 and 104 show working
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To find out the perimeter of a triangular region, what formula would you use? The perimeter of a triangle is length of surface a plus length of side b plus length of side c.
Now we need to move onto something called function notation. Function notation will be utilized heavily throughout most of remaining section and so it is important to understand i
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