Where is the function continuous? Differentiable? Use the grap...

Question

Where is the function continuous? Differentiable? Use the graph of f in the figure to do the following.

c. Sketch a graph of f'.

Accepted Answer

Welcome back, everyone. In this problem, the graph of a function Y equals JX is given below. Use this graph to draw the graph of its derivative J X. Here we have the graph of G of X. And then we have a blank graph on which we're going to draw the derivative, OK. So how are we going to do that? How, how can we figure out the graph of derivative just by looking at the graph of our function? Well, if we can look at our graph and identify regions where the slope is positive, negative, or zero, then the slope of J at any point corresponds to the value of J at that point because remember our derivative of X is really just the rate of change or or the slope with respect to X for J. So let's look at the different parts of our graph to see if we can figure out how our slope behaves. Now notice, starting from X equals 0 to X equals 2, or curve, or sorry, J X goes from Y equals 2 to Y equals 6 and the slope is positive. So that means J will be above the x axis. It will also have positive values. So now, if we do the same here, then starting at X equals 2 and going to where sorry, starting at Y equals 2 when X is 0 to Y being equal to 6 when X is 2. Then we have our points. We know that when X equals 6, let's put that properly here. Sorry, when, when X equals 2. At Y equals 6, that's gonna be open. OK? Now that we have our points, we can draw or. Or or or a slope. So this is gonna be our slope when, sorry, between X equals 0 to X equals 2 for J. Next, if we go back to our graph, notice that from X equals 2 to X equals 4, our slope is negative. And in regions where the slope of J is negative, J will be below the x axis. Notice that it goes down by 4 units. So now, starting at that point here. Where X equals 2, and again, this will be open. It's gonna go down by 4 units to where X equals 4. So X E equals 41234. That's gonna be here and then we can draw our line, OK? Now, let's go back to our graph. What, what else do we notice? Well, no, notice that from X equals 4 to X equals 6, the slope is constant. So the graph of the function is going to be a straight line that is gonna be equal to our slope here. So what is this slope going to be? OK. Well, from X equals 4 to X equals 6. Then notice that our slope M is going to be equal to the difference between the Yordinates, that's 8 minus 3, divided by the difference between the X-ordinates, 6 minus 48 minus 3 equals 56 minus 4 equals 2, so our slope is going to be 2.5. So now if we go to the graph of our derivative, OK. Then starting from 4 where it's open, we're gonna go to 2.5 and it's gonna continue to 6. This is going to be the graph of the derivative of J of X. Thanks a lot for watching everyone. I hope this video helped.

Where is the function continuous? Differentiable? Use the graph of f in the figure to do the following. <IMAGE>
c. Sketch a graph of f'.

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Where is the function continuous? Differentiable? Use the graph of f in the figure to do the following. <IMAGE>c. Sketch a graph of f'.

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Where is the function continuous? Differentiable? Use the graph of f in the figure to do the following. <IMAGE>
c. Sketch a graph of f'.