If the showerhead is used for 0 minutes, how many gallons of water will be used? What ordered pair represents this situation? What is
this location called?
broove no one is using the showers

Given: f(x) = 9 cos(2x)

The differential is
df = - 18 sin(2x) dx

When x varies from π/6 to π/6 + 01, then dx = 0.1.
The change in f is
δf = - 18 sin(π/3) *(0.1) = -1.5588 ≈ -1.559

If we compute the change in f directly, we obtain
f(π/6) = 9 cos(π/3) = 4.5
f(π/6 + 0.1) = 9 cos(π/3 + 0.2) = 2.6818
δf = 2.6818- 4.5 = -1.6382 ≈ -1.638

Direct computation of δf is close to the actual value but in error.
The two results will be closer as dx gets smaller.

δf = -1.559  (correct answer)
δf = -1.638 (approximate answer)