WEBVTT
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Use the given graph of đť‘“ to find the coordinates of the points of inflection.
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Well, to understand how to solve this problem, we need to know what are the points of inflection.
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Well, the points of inflection are actually the points where there is a change of concavity.
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So what I actually mean by a change of concavity is where the shape of our function changes.
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So it can change from concave down to concave up or concave up to concave down.
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So in order to find our points of inflection, weâ€™re gonna have a look at our graph and actually see where itâ€™s concave up and concave down.
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Well, we can actually see in this first section our function is actually concave down.
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And then, we change to a section which Iâ€™ve marked in pink, where we can actually see that the function is concave up.
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And then, we have another section of marks in orange, which is a short section of concave down.
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And then, finally, the last section of our function in the graph is actually concave up.
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Okay, great, so we now marked on the concave down and concave up segments of our function.
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So this is where we go back to our definition because we now want to find the points of inflection.
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And we can see that actually the points of inflection are the points, where the concavity actually changes.
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And Iâ€™ve marked on with red crosses where the concavity changes.
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You can see we go from concave down to concave up and then concave up to concave down and back from concave down to concave up.
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So therefore, we can actually say that the points of inflection are the first point two, two and thatâ€™s because we change from concave down to concave up.
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Our second point is four, three and thatâ€™s because we change from concave up to concave down.
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And then, our last change in concavity is at our final point five, four.
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So therefore, there are three points of inflection.