00:01
So here we want to find the difference quotient where our function is negative 2x squared plus 4.
00:05
So we first need to find f of x plus h.
00:09
So that means we're going to take x plus h and plug it in wherever we see an x.
00:14
So we're going to have negative 2 times x plus h squared plus 4.
00:19
This is then going to equal negative 2 times x squared plus 2xh plus h squared when expanded and then plus 4.
00:29
Distributing that negative 2 to each of the terms, so x squared 2xh and h squared, we're going to get negative 2x squared minus 4xh minus 2h squared plus 4.
00:45
So if we plug this into our difference quotient, we're going to get negative 2x squared minus 4xh minus 2h squared plus 4.
00:56
That's our f of x plus h.
00:58
Then we're going to subtract our f of x, which is just that negative 2x squared plus 4.
01:07
From here, we then need to divide all of that by h.
01:13
Distributing the negative is then going to result in a, well, negative 1 times negative 2x squared is going to give us a positive 2x squared.
01:23
And then a negative times a positive 4 is going to give us a negative 4...