00:01
Okay, here in blue is the curve y equals x cubed, and in red, a tangent line at the point 1 .1.
00:10
And the first thing we do is find the equation of this tangent line.
00:17
Well, we know that y is x cubed, which means dy by d x is 3x squared.
00:27
And then when x equals 1, as it is here, d .y by dx will be 3 times 1 squared or 3.
00:42
Now that is my tangent slope at the point 1 .1.
00:48
So i know then here, m my slope is 3.
00:54
So for a line, we know the equation is y equals mx plus 1.
01:00
B and to find b, no end is 3, so y equals 3x plus b.
01:11
And to find b, plug in the point 1 -1 on the line.
01:16
So 1 equals 3 plus b, b is minus 2.
01:22
Which means my line equation is y equals 3x minus 2.
01:33
Now next i want to figure out this.
01:37
Point here where the curve and the line meet.
01:42
So x cubed is the curve has to equal 3x minus 2.
01:51
That you can solve with the calculator.
01:53
Just graph it and see where they meet and you'll find that x is equal to minus 2.
02:03
If you check you can see minus 2 cubed is minus 8 and 3 times minus 2, minus 2 also minus 8.
02:12
So we now know then at this point here is minus 2.
02:19
Now i want to work out this area in green here between the curve and the tangent...