00:01
Okay, suppose i have the function f of x, and i want to find the slope of the tangent line at x equals 1.
00:13
So at this point on the line, i want to find the slope of the tangent line.
00:16
Okay, slope of the tangent line, what is that we've given this function at a point? i could draw a tangent to that function, and i want to find the slope of that line.
00:25
Whenever i see slope with the tangent line, i'm really talking about the derivative at a point at x equals 1 in particular.
00:32
Okay, so how do i find the slope? well, i find the first derivative, which is just f of x plus h, minus f of x, all divided by h.
00:44
So in my function, i could just replace x with x plus h minus whatever f of x is, which is 4x plus 2, all divided by h.
00:59
What i could do here is distribute this four to both terms, 4x plus 4h plus 2.
01:06
I know i'm distributing the negative here minus 4x minus 2.
01:10
I can cancel what's common.
01:12
And i'm just left with 4h divided by h, which is just 4.
01:17
So the slope of just my function in general is 4.
01:21
If i were to plug in 1 into this function, well, there is no x value...