Slope

That's the slope of the slope, or the rate of change of the slope itself.

The sloping roof.

The slope was increasing.

Slope decreases.

They have come to the top of a cliff.

So our slope has decreased.

Slope is decreasing.

The slope was very positive.

The rate of change of the slope is negative.

Throw me off the cliff!

One, they said, Life is on an incline.

We made the last one. I know.

Yes, for over there on the steep side.

So what did we say about concave upwards? concave upwards is when the slope is increasing, which means that the rate of change of the slope is positive.

If the slope is constantly increasing, then the rate of change of slope is positive, then the second derivative is positive.

If the slope is decreasing, then the rate of change of slope is negative, which tells us that the second derivative is negative.

If only we had some sort of ramp... ding

So as we increased x, the slope increased.

And as we increase now, our slope becomes negative.

Our slope was decreasing up until this point.

Now, in concave downwards, the slope is decreasing.

A time when you can't tell between the road and a cliff.

It would have been so easy. Remember the precipice?

There are dizzy daffodils on the hillside

Then we come to the rapids?

Hendricks and his men are headed for the rapids.

Fiske, Vicente, watch that end of the ridge.

You spawn of the devil's own strumpet!

And then after that point, our slope is increasing.

At the bottom of the cliff, we find that they're rare as hens' teeth.

Distance would be the height of the cliff, and so how do we figure this out?

And on this cliff, I have a car.

Dr. Edwardes plunged over the precipice while skiing.

We pass the face of that cliff.

We are crossing a snow bridge. Three men on a rope.

Bellied up a ridge, and there they were, right below me.

She might have fallen from these cliffs.

The South Cliff.

You will be there?

There's the Curwen palace over there on the cliff.

So at that point, the slope of the tangent line, or the slope of the actual graph, or the instantaneous slope, however you want to view it let me see how well I can draw it it'll look something like that, and that's the tangent line.

That's what we've been graphing. f prime of x, that's the slope of the function, slope of function at any point x.

Now, at the base of the high cliffs there's this natural cave.

At that x value, the slope looks like that.