WEBVTT
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we are going to sketch the graph of the function
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sine of X. For X greater than or equal
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to zero. And lessons I have. And is
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that graph to find the absolute and local maximum and
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minimum values of the function. So we know that
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the sine function At zero is equal to zero and
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then it is increasing from zero to buy half that
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by healthy. It has a value one but in
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this case is not included in the graph. So
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we can say that we have something like this.
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Okay. And this corresponds to by half here mm
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Value one. She'll be a little bit more flatten
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around here but it's not probably Okay. So we
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can say that the by the one should be around
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and mm should be around here. Everything right?
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So to indicate and describe that the image of my
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half Which is one. Normally it's not included because
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the enjoyed something. We have this and here at
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zero is included. So we do this type of
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graphic sign to indicate that. Yeah. So we
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can see that F. That's the formula to remember
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. We're talking about sign of eggs. For eggs
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. Okay, there we go to zero but less
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than by half. And so we have effectively we
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have uh absolute minimum at zero and the value zero
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. So F zero equals zero is the absolute minimum
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of minimum value of F on zero. I have
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zero. Close by. Have opened is the absolute
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minimum there's no relative minimum because this is a satirical
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Syria cannot be considered local because we have no uh
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function to the left, even though the sign is
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defined, we have considered only on that internal,
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so there is no local minimum, have has no
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local meaningful on that interval. Uh We respected the
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absolute maximum of local maximum, there is neither one
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of them because we have opened this interval here,
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there is, there is not a maximum or highest
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point on the graph because the point is not good
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. So if has no local or absolute maximum.
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And so this is the behavior as a function sine
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of X for X greater than or equal to zero
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, but less less than by half. There is
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an absolute minimum value of zero at 0 and there
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is no local minimum, no local maximum, no
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absolute maximum.