00:01
In this question, we want to find the equation of a tangent to the graph f of x at x equals 1.
00:05
So let's find the slope of our tangent line by using the limit definition of a derivative, where limit of h is approaching 0 of f of x plus h minus f of x minus f of x over x over h.
00:18
Here we have x equals 1.
00:20
So if we plug this all in, we get 2 over 1 plus h minus f of 1 will be 2 over h.
00:28
What we want to do is we want to make a common denominator, what we have here.
00:32
So we'll have everything over age still, but for this we'll have 1 plus h.
00:36
This 2 is still the same, but we make this 2 a fraction with multiplying the numerator and denominator of 2 by 1 plus h.
00:44
So we have 2 times 1 plus h, which is 2 plus 2h.
00:49
And what we can do now is just simplify this.
00:52
So we have 2 minus 2 plus 2h is just minus 2h.
00:58
1 plus h and h.
01:00
So if we cancel out these hs and we get negative 2 over 1 plus h...