Whatever function value I get at the positive value of number,

I'm going to get the same function value at the negative value.

So what's the average value of a function?

Something is only a function if for a given x value, you only have one y value.

Well, if we look here, the value of the function is

But in general, you could approximate a function around any value.

So you can actually get rid of that absolute value function there.

So the minimum value that the function could take on is 1.

Say, here, I'll put it into the function and it'll give us a z value now.

But then they ask us, well, what's the average value of the function?

So we'll make the value under the curve as a function of y.

The height is the value of the function, which is x y squared.

And the sine of theta is the y value on the unit function on the unit circle.

Form and function.

For a function, for any given x, you can only define one y value.

So when x is equal to 0, what is the value of this function?

But having a positive slope means that the value of the function is increasing.

Whatever the x value is you just put into this f prime of x function or the derivative function, and you'll get the slope at that point.

So the magnitude of the x direction is just a function of your y value.

If it's always going to be the same value, you're dealing with a linear function.

And the absolute value divided by the absolute value.

The slope of the secant line is equal to the value of the function at this point, f of x naught plus h, minus the value of the function here, mine f of x naught.

The slope at any point of this curve is equal to the value of the function.

Remember, there's a difference between book value and market value.

Well, here we have the derivative, the derivative is actually a function of both the x and the y value.

Now, the mean value theorem tells us that if this function is defined on this interval, and it is, right?

It's going to be a function of two parameters, s and t, and it's going to be equal to its x value.

All value is perceived value.

Because another way to think about it, if you just took the average value of the function so if the function was, say, this, and you just multiplied that average value times the base, you would get the same area as the integral.

There is the cosine function, and there is the tangent function.

The limit, as x approaches this value, is indeed equal to the function evaluated at that point.

Just like we said before, the volume above it is equal to the value of the function.

A function, we said, if you give me any x value, I will give you an output.

The slope at any point of that line is equal to the x value is equal to the function at that point, not the x value.

Function