00:01
Hi there, so for this problem we need to use the limit definition of derivative to find the derivative of the function f at 3.
00:13
This when the function f of x is given and that it is x minus x square.
00:22
Then with that said, we know that the definition of the derivative of a function is just the limit.
00:35
When h tends to 0 of the function evaluated at x plus h, and this minus the function f of s, and this divided by h.
00:50
So let's do that in here.
00:53
The first find the derivative of this function by definition.
00:58
So that will be the limit when h tends to zero, and then this is the function evaluated at a, x plus h so that will be x plus h for the first term and then this minus this minus x plus h and that to the square and then we will have this minus this minus the function f of x so that will be x plus x square and then we divide this by h now let's see what we obtain from this.
01:42
So we will have the limit when age tends to zero.
01:47
Then we will have x plus age.
01:51
We can already cancel this with this.
01:55
So we will have just simply age in here...