00:01
Okay, so here's the curve 2 minus x squared, 2 minus x cubed, excuse me, and then we want the slope of the line tangent to this curve at 1 -1.
00:16
Okay, so we just do the same thing.
00:19
We look at 1 plus h, the value of the curve at 1 plus h, and then subtract just the curve evaluated at 1, and then all over h, and then simplify this out and hope that we can see what has.
00:37
Happens when h gets really really small as this as that siket line kind of converges into the tangent line so we have two and then so this is a this is a binomial cubed so we can use kind of pascal's triangle i mean you can just distribute it out but this should be one plus three h plus three h squared plus h cubed again, i'm just using binomial expansion, pascal's triangle, or you can just kind of foil out all those terms.
01:25
And then minus 2 minus 1 cubed, which is just 1 all over h.
01:36
Okay, so this is 2 minus 1, so that's 0...