00:01
Okay, here is the function y equals f of x, and it gives you f dash of x at the first differential.
00:07
I want to work out where the function is increasing.
00:10
What that means is it's going uphill all the time from left to right.
00:15
That's an increasing function.
00:17
So you can see that the slope of the function is always plus.
00:23
So here then the slope, or do y by d x, is always bigger than zero.
00:30
If the function is increasing.
00:33
It's decreasing, it's going downhill left to right, and we have a negative gradient.
00:39
So here then what i want is f -dash -of -x bigger than zero.
00:44
So this then bigger than zero for f to be an increasing function.
00:55
Now, the top part of it, x plus 1 squared, is always bigger than 0, except when x is negative...