The depth of water (in meters) in a tide pool from midnight ( hours) until 8:00 a.m
MATHEMATICS · Multi-part · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation
Problem
The depth of water (in meters) in a tide pool from midnight (t=0 hours) until 8:00 a.m. (t=8 hours) is modeled by the piecewise function
D(t)={0.5t+1,−0.5(t−4)+3,0≤t≤4,4<t≤8.
Throughout this problem, interpret t in hours and D(t) in meters.
(a) Show that D is continuous on the interval [0,8]. Your argument must address the point where the formula changes.
(b) Explain whether the Extreme Value Theorem guarantees the existence of both an absolute maximum depth and an absolute minimum depth for D on [0,8]. Justify your answer by explicitly referencing the hypotheses of the theorem.