00:01
We want to find all the values of x where there is a tangent line to this curve that will be horizontal.
00:07
So the curve is f of x equals x cubed minus 3x squared minus 8x plus 19.
00:18
So we're going to have this curve.
00:20
I'm just going to draw a mock of the curve.
00:23
And i'm looking for the places where we have horizontal tangent lines.
00:28
And when we're talking about tangent lines, we're talking about slopes being zero.
00:34
So to talk about slope, we have to find a derivative.
00:37
So therefore, the derivative of this function will be 3x squared minus 6x minus 8.
00:48
And if the tangent lines are horizontal, then their slopes would be zero.
00:54
So that means i need the derivative to be zero.
01:16
So i'm going to set 3x squared minus 6x minus 8 equal to 0.
01:24
So i will need to use the quadratic formula, and the quadratic formula is x equals negative b or opposite of b, plus or minus the square root of b squared minus 4ac all over to a...