Question

A point P is moving on the curve y = 2x2. The x coordinate of P is increasing at the rate of 4 units per second. Find the rate at which the y coordinate is increasing when the point is at (2, 8).

Answer 1

dx/dt=4 (given)
y= 2x^2
dy/dt= (4x)dx/dt
[dy/dt] at (x=2) =4×2×4=32 unit/sec

Answer 2

A point P is moving on the curve y = 2x² .

it is given that, x coordinate of P is increasing at the rate of 4 units per second.

e.g., dx/dt = 4 unit/sec

we have to find the rate of y coordinate is increasing when the point is at (2,8)

differentiating curves with respect to t,

dy/dt = 4x dx/dt

at (2, 8) , dy/dt = 4 × 2 × 4 = 32 unit /sec

hence, rate of increasing of y - coordinate is 32 unit/second