Answer:
3√21 units/second
Step-by-step explanation:
Let s', x', and y' represent the derivatives of the respective variable with respect to time. We are given s' = √210 units/second, and we want to find y'.
We also have the relation ...
(s')^2 = (y')^2 +(x')^2 . . . . . from the Pythagorean theorem
We can differentiate the given equation for y to get ...
dy/dx = 2x -1 = 2(2) -1 = 3 . . . . . at x=2
We also know ...
y' = (dy/dx)(x') = 3x'
x' = y'/3
Using this in the above equation for s', we get ...
(√210)^2 = (y')^2 + (y'/3)^2 = (10/9)(y')^2
(9/10)(210) = (y')^2
3√21 = y'
The value of dy/dt is 3√21 units per second at the point (2, 2).
