A balloon’s height above the ground is modeled by a differentiable function

MATHEMATICS · Subjective · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation

Problem

A balloon’s height above the ground is modeled by a differentiable function h(t)h(t), where tt is measured in minutes. Suppose • h′(t)>0h'(t)>0 for 0<t<120<t<12, • h′(12)=0h'(12)=0, and • h′(t)<0h'(t)<0 for t>12t>12. Explain what happens to the balloon at t=12t=12 minutes and why.

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