The figure shows the curve y² = 2x. The points O (0,0) and P(x, y) lie on the curve. Given that the coordinates of Q is (x, 0),
(a) express the area, A cm², of the triangle OPQ in terms of x.
(b) If x is increasing at a rate of 4 units per seconds, calculate the rate of increase of A when x = 2.
*************************
Answer:
(a) Area of triangle OPQ, A = ½(OQ)(PQ) = ½xy
y² = 2x
Since area of triangle is positive, we take the positive value of y
Hence,
(b) Using product rule,
If x is increasing at a rate of 4 units per seconds, then dx/dt = 4.
When x = 2, dA/dt = 6(2) / √(2)(2)
= 6
