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Consider the function whose graph is sketched:Find the open intervals over which the function is increasing or decreasing: Write the answers in interval notation: T...

Question

Consider the function whose graph is sketched:Find the open intervals over which the function is increasing or decreasing: Write the answers in interval notation: The open x-intervals over which the function is increasing: The open x-intervals over which the function is decreasing:Function has local maximum at xFunction has local minimum at x =

Consider the function whose graph is sketched: Find the open intervals over which the function is increasing or decreasing: Write the answers in interval notation: The open x-intervals over which the function is increasing: The open x-intervals over which the function is decreasing: Function has local maximum at x Function has local minimum at x =



Answers

Use a graphing utility to graph the function and (b) determine the open intervals on which the function is increasing, decreasing, or constant. $$f(x)=x$$

The given function is half off. X is equal to acts. In the first part. The graph off the function will be like this F off X is all of this in crazy? In the second part, the function increases on minus infinity do insanity.

We want to find where the function F of X is increasing or decreasing. And then we want to identify those intervals on the graph of F on the left, so F of X is equal to negative, expose one square. In order to find what affects increasing or decreasing. We use the first derivative. So we'll go through step by step to make sure we understand we're together. First, we need to find F prime X. So F prime X is simply negative to expose one. This is by the chain rule. Next we identify the critical points of F. Prime. This is where it's equal to zero and define the critical points occur at X equals negative one. Next we have to conduct a sign charts. We have to check the sign of a crime left and right of negative one. So to the left of X equals negative one, which is technical negative time prime is positive. Therefore F is increasing there to the right, prime is negative, so that's what F is decreasing. Thus we have increasingly negative three negative one, decreasing the negative one to infinity. And these colors match with the areas where F is increasing or decreasing on the left.

We want to identify with the function after taxes increasing or decreasing function F X equals X squared over X plus one. We then want to identify on the graph where that is the case. So we're gonna use the first derivative of F to figure out what it's increasing or decreasing. That means that the first time that derivative. So F climaxes extends exposed to over expose one square. This is using the quotient rule and simplifying. Next. We defend the critical points of F. That's where the function is defined undefined and equal to zero from the denominator we get X equals negative one is a critical point and from the numerator is equal to zero. We get technical negative to zero. Now we have to test F. Prime for the sign and all intervals. So to the left of negative two's technical negative 10 and time is positive. Therefore increasing between negative to negative one negative, decreasing between negative +10 negatives are decreasing and to the right of zero positive. So increasing so F is increasing on negative negative negative two to infinity, decreasing the negative to negative one and negative +10 We can identify this on the graph of F. I think it's decreasing. Yellow is increasing.

If we have the function F of X equals X plus three squared. If it helps, you can sketch, it is going to be shifted to the left three and then that's when the axis, that's what the vertex is. So you can then accordingly do the pattern and reflect points. But it's at that vertex where change happens, we're increasing to the right of it and decreasing to the left of it because you read it left to right. So for part A That it described interval our exes it's from -3 to infinity. That it's increasing And from negative infinity to negative three where it's decreasing.


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