00:01
For this problem, we want to find the values of a and b, if we're given y equals b times x times a square root of x, and the tangent line to this curve is 5x plus 2y equals a at the point x equals 9.
00:15
Now we know that our y prime is equal to the slope of the tangent line.
00:21
So if our y is equal to b times x squared of x, which is also b times x, x squared of x, which is also b times x, raised to three halves, then our y prime is equal to b times 3 over 2 times x raised to 1 half.
00:39
And if our 5x plus 2y equals a is our tangent line implies 2y equals negative 5x plus a, or that y equals negative 5 halves x plus a over 2, then y prime equals m tangent implies that b times 3 over 2 times x raised to 1 half, that's equal to negative 5 over 2.
01:16
If x is equal to 9, this implies that 3 halves b times 9 raised 1 1ā2 equals negative 5 over 2.
01:28
And if we solve for b, b is equal to negative 5 over 2 times 2 thirds times square root of 9 for this.
01:42
So it will be 3.
01:44
So we'll divide this by 3...