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You are glven the grph of a function delinco the Interval(-~,0) Flna the coordinates of Lhe absolutc entcr DNE ) maxlmum and the absolute minimum of 6 M Incy '...

Question

You are glven the grph of a function delinco the Interval(-~,0) Flna the coordinates of Lhe absolutc entcr DNE ) maxlmum and the absolute minimum of 6 M Incy ' cxist (Il an ansiycr doos not oxlst;moxlmumminimvm

You are glven the grph of a function delinco the Interval(-~,0) Flna the coordinates of Lhe absolutc entcr DNE ) maxlmum and the absolute minimum of 6 M Incy ' cxist (Il an ansiycr doos not oxlst; moxlmum minimvm



Answers

Find the maximum and minimum values of the function. $$y=2 \cos \left[3\left(x-\frac{\pi}{2}\right)\right]+6$$

The given function as my equals one by to sign off do eggs minus six time and less for a base for in China sane. And to find the maximum and minimum, we care about amplitude. But it's one by two on the shift in the Via Coordinate that does my four units downwards. So the maximum of our base function as one. Therefore, the maximum off given function right would be amplitude diets Max off base minus to shift. That does minus 3.5. No minimum. Most annex we know as minus one. Therefore, minimum off. I would be again amplitude named the minimum off base. My next chef that does. He will do my best for five units.

We are trying to find the absolute extreme of for this function on the given interval first let's determine the critical numbers The derivative of our function. If we bring the two thirds out front, that would give us 6/3 or two And then we will subtract one From the power. So this is two over the cube root of fada critical numbers would occur either where H prime is zero or where the function is not differentiable. Well H prime is never going to be zero because fractions are zero at the top of zero. But we have a top value of two. It is though non differentiable when the denominator zero And that is very obviously zero When data is zero. So let's take a look at the values of the function at the end points and at the critical point. Oh yeah If we fill in -27 for data into the original function, the cube root of negative 27 is negative three, negative three squared is nine. And then we have at times three out front. So that would give us 27. zero will give us zero and for eight we feel an eight cuba motivate is too Two squared is four and then we have the times three out front, which is 12, so the smallest value is zero. And that occurs when data is zero. That's our absolute minimum. Our largest function value is 27 And that occurs when data is -27.

For this question were given HFC that is equal to three. Data to tooth. There's power in the drivel were negatively seven is lost your equal fado just lost equal to eight. Those set off what's going to look for any critical numbers. So we have a chip card with ADA is equal to We can use our part role slots that we have to data neither 1/3 power. So then we have votes on Tuesday to honor the 1/3 power is equal to zero. Was any of a critical numbers. We know that this is never true. So therefore we consider absolute maximum minimum values are on our own points of intervals. So we have eight of 1927 is equal to three times 10 to 27 to the 2/3 power, which will get us 27. Then we have each of eight, which is equal to three times date. 2/3 power, which will get us 12 so we can say that are absolute been wrong. Is 12 at X is equal to eight. No absolute maximum is 27 at X is equal to negative 27

For this question we have enough data is because the sign of data on the interval from the good property was lost illegal. That data, which is lost in April to five pi over six when we asked if I know absolute max wounds of my bones on this interval. So this about foots when you find critical values of primary data, which is equal to co Santa Fada, it's honest Interval. What we can say concentrate is equal to zero when they uh So what if a that is equal to, Let's see, we have negative pi over two and then we have pi over two. And so then the next thing we need to do is we need to find use your incredible numbers and our side Wellies were also fun after maximum minimum. So we have us. Uh, let's see neither pi over two. It's a sign of prying neighbour pi over two, which is equal to negative one. We have half of pirate or two people to sign a part or two. We're Jews equal to one. Then we have the sign. So it's Assam five pi Over six. She was a sign of far higher over six, which is you. Go to 1/2 so we will get my absolute minimum. And I have one in our absolute max along not one.


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