During an uninterrupted trip

MATHEMATICS · Subjective · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties

Problem

During an uninterrupted trip, the volume of fuel in a car’s tank is modeled by L(t)L(t) gallons, where tt is the number of hours since departure. The rate of fuel consumption L′(t)L'(t) exists and is continuous for 0≤t≤T0\le t\le T. Give a mathematical reason, stated in one sentence, why L(t)L(t) must be continuous on [0,T][0,T].

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