00:01
In this question, we are asked to find the derivative of the function f by using the definition.
00:05
And first, we need to calculate f of x plus h.
00:09
To get f of x plus h, we simply need to replace x in the formula for f by x plus h.
00:19
And we are going to get 2 times x plus h squared plus 9 times x plus h.
00:27
And now let's expand this expression.
00:30
We are going to get 2 times x squared plus 2xxx plus h squared plus 9x plus 9h and then we are going to get 2x squared plus 4xh plus 2h squared plus 9h plus 9h next we need to calculate f of x plus h minus f of x plus h is we will just copy it from the previous line and from that expression we need to subtract f of x, which equals to 2x squared plus 9x minus 2x squared plus 9x.
01:31
Well, 2x squared and 9x cancel.
01:36
And the whole expression, the difference simplifies to 4xh plus 2h squared plus 9h.
01:44
So that's the difference, f of x plus h minus f of x.
01:51
Now we need to calculate the difference portion...