A hot air balloon is launched into the air with a human pilot. The twice-differentiable function...

    

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A hot air balloon is launched into the air with a human pilot. The twice-differentiable function h models the balloon's height, measured in feet, at time t, measured in minutes. The table above gives values of h(t) at selected times t. t 0 10 30 minutes h(t) 0 100 80 feet 00 40 85 95 flat The turice differentiable function h mode 1. For 10 t 30, must there be a time t when the balloon is 81 feet in the air? Justify your answer. 2. For 30 st 40, must there be a time t when the balloon's velocity is 2 feet per second? Justify your answer. Using the Mean Value Theorem, find where the instantaneous rate of change is equivalent to the average rate of change. Round/truncate to three decimal places where necessary. B. y=x2-x+1 on [-2,1] 4. y = cos(x) on 5. y = (4x + 24) on [-6.-2] A hot air balloon is launched into the air with a human pilot. The twice-differentiable function h models the balloon's height, measured in feet, at time t, measured in minutes. The table above gives values of h(t) at selected times t. t 0 10 30 minutes h(t) 0 100 80 feet 00 40 85 95 flat The turice differentiable function h mode 1. For 10 t 30, must there be a time t when the balloon is 81 feet in the air? Justify your answer. 2. For 30 st 40, must there be a time t when the balloon's velocity is 2 feet per second? Justify your answer. Using the Mean Value Theorem, find where the instantaneous rate of change is equivalent to the average rate of change. Round/truncate to three decimal places where necessary. B. y=x2-x+1 on [-2,1] 4. y = cos(x) on 5. y = (4x + 24) on [-6.-2]