00:01
If we think about what the graph of this function looks like, it's just a downward opening parabola with its vertex at the origin.
00:13
So at x equals negative 3, the slope of the tangent line, right? slope of the tangent line should be positive.
00:29
At x equals 0, the slope of the tangent line should be, 0, neither positive nor negative, and at 1, the slope of the tangent line should be negative.
00:50
Now we want to find the actual slope of the tangent line at those points.
00:55
So we're going to get the derivative of this function, which is going to give me just negative 3x.
01:02
When i use power roll, f prime of negative 3 is negative 3 times negative 3.
01:11
Or negative or positive, sorry, positive 9.
01:17
F prime of 0 is just negative 3 times 0 or 0.
01:24
And f prime of 1 is just going to give me negative 3 times 1, which is negative 3.
01:32
So that's consistent with what we saw from the graph.
01:35
Now we want to find the equation of the tangent line at negative 3.
01:42
Well, i have the slope, and that is 9...