Interpreting the derivative The graph of f' on the interval [-...

Question

Interpreting the derivative The graph of f' on the interval [-3,2] is shown in the figure.

a. On what interval(s) is f increasing? Decreasing?

Accepted Answer

Welcome back, everyone. The figure shows the graph of F on the closed interval from -6 to 3 inclusive. Determine the intervals on which F is increasing and decreasing. So we want to recall that a function F of X is increasing if its derivative is positive. So let's analyze this case. Now we're given the graph of the derivative. So where is it positive? Well, above the x axis because those are the positive values for F of X. And we can clearly see a region where the graph is above the x axis, right? So essentially we can see that from 6 up to -4 it's positive. At -4 it's actually 0. However, the function's derivative is still positive, so we classify it as a saddle point. Because the derivative doesn't change its sign, so we can actually include -4 within our interval because it's a saddle point and only at X equals -1, this is where the derivative becomes negative. So we can conclude that the function is increasing when. X belongs to the interval from -6 because that's the end point we're not including it in the interval. So from -6 up to -1, not inclusive. This is where the function is increasing because the derivative is positive. Now if FFX is decreasing. This means that the derivative of F of X is negative. Now where is it negative? Well, from -1 onwards, so x belongs to the interval. From a -1 not inclusive because this is the point of Maximum, right, because the function was increasing and started to decrease, so we're not including any extrama points. So from -1 up to. X equals 3. Once again, not inclusive because that's the endpoint of the interval, and that's it. We have our answers, so the function is increasing. When x belongs to the interval from -6 up to -1, not inclusive, and the function is decreasing, when X belongs to the interval from -1 up to 3, not inclusive. Thank you for watching.

Interpreting the derivative The graph of f' on the interval [-3,2] is shown in the figure. <IMAGE>

a. On what interval(s) is f increasing? Decreasing?

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Interpreting the derivative The graph of f' on the interval [-3,2] is shown in the figure. <IMAGE>a. On what interval(s) is f increasing? Decreasing?

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Interpreting the derivative The graph of f' on the interval [-3,2] is shown in the figure. <IMAGE>

a. On what interval(s) is f increasing? Decreasing?