Let y = 4x^2. Find the change in y, Δy when x = 3 and x = 0.2. Find the differential dy when x = 3 and dx = 0.2.

Question

Let y = 4x².

Find the change in y, Δy when x = 3 and Δx = 0.2

Find the differential dy when x = 3 and dx = 0.2

Answer 1

If y = 4x² then y(3) = 4(3)² = 36

If we increase x to 3.2, then y(3.2) = 4(3.2)² = 40.96 so Δy = 40.96 - 36 = 4.96

If y = 4x² then dy/dx = 8x (using the power rule). So dy = 8x•dx = 8(3)(0.2) = 4.8