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Identify the function's local and absolute extreme values, if any, saying where they occurX-1h(x) = X + Sx+10...

Question

Identify the function's local and absolute extreme values, if any, saying where they occurX-1h(x) = X + Sx+10

Identify the function's local and absolute extreme values, if any, saying where they occur X-1 h(x) = X + Sx+10



Answers

Find the absolute maximum and absolute minimum values of f on the given interval. [0,6]
f(x) = x/x^2-x+4

Well, look at the time was that those bond on this bomb here is empty and it's your time. So empty. So there's an empty means. Never be no absolute maximum. Nelson isn't organized then? No. Absolute minimum. So this one with me? No, I'm sort of like UMA.

So look in the graph, we seem down. The function attends the maximum and despondency here socially absolute. I'm so maximum ack ack say, could you see and find, um, accurate minimum? We have because of this bone here near absolute minimum. Andi. Thanks. Go to be on ga Extreme burial Tomb can be a blind because the function F accident is continuous on into movement, I should be.

So look at the ground. We see that we have this point here. We mean absolute. The next one on the front. Thanks In could you see from the oven? Absolute minimum. We don't hire because those bone here is empty vision. Answer empty. So doesn't it means then will be no absolute minimum.

So here in this problem we have to find the absolute maximum and absolute minimum for the function F of X is equal to X over X squared minus X plus four in the interview. 0 to 6. First of all, it will be differentiating this function. So we'll be calculating f premix. So if premix is equal to we can use questions rule here. So X square minus X plus four whole square dysfunction as it is, X square minus X plus four times the transition of this function, which is one minus dysfunction as it is times the differentiation of dysfunction is works minus four minus one. Sorry? So I will get a frameworks as minus X square plus four, divide by this is X square minus X plus four. Hold square. Now will be calculating the critical points for that will be subsiding if premix as it calls to zero, that means they should be called to zero. So from here will get the value of X s plus minus two since minus two is not in the interval. So we have only one critical point that is X equal to two. Now we'll be checking the value of F of X at zero at X equals to zero two. And then six. So we'll get f of zero as this would be zero over zero square minus zero plus four. So it would be called to zero. The next will be evaluating for F of two, will substitute access to so to over two square minus two plus four. And we'll get this value has won over three and finally F of six will be called to 3/17. We have just blocked X. S. Six and then we are playing this number. So from here we can conclude that absolute maximum is this value. So one by three an absolute minimum is zero. So there's a final answer. I hope you have understood the problem. Thank you.


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