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Current time:0:00Total duration:3:16

- [Voiceover] So part c. Find the x-coordinates of
all points of inflection for the graph of f. Give a reason for your answer. So points of inflection, points of inflection happen when we go from concave upwards, concave upwards to downwards or vice versa. So this is true if and only if f prime prime of x goes from positive to negative or vice versa. So where do we see f prime prime of x going from positive to negative? Well that's going to
be true if and only if f prime of x goes from being increasing to
decreasing or vice versa. F prime goes from increasing to decreasing or vice versa. We're seeing a lot of vice versa here. So now let's, and I
want you to think of it in terms of f prime because
we have the graph of f prime. So f prime goes from
increasing to decreasing or vice versa or we could go
from decreasing to increasing. Let's think about it. Let's see, over here, f prime is decreasing, decreasing,
decreasing, decreasing and then it increases. So we have a point of inflection
right over here, right? When f prime of x is zero. That's because a prime is differentiable so the derivative is definitely, the derivative is zero right at that point of inflection right over here. So with that happens at
x equals negative one. And over here, then f
prime starts increasing but then right at x equals one then it starts decreasing. So at x equals one, we have
another point of inflection. That's where we have that zero, that zero of tangent line with slope zero. And then we're decreasing, decreasing, decreasing, decreasing,
decreasing, increasing. All right, so this is going to be another point of inflection, x equals three. So these are at three
points of inflection. So this happens, happens at x equals negative one, x equals one and x equals three. So these three points
on our graph of f prime where we see f prime goes
from decreasing to increasing or increasing to decreasing
or decreasing to increasing. All right, all right. Now, well, I'll do the last
part on the next video.

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