Which of the following do you think is closest to the temperature at 515am A 2

# Which of the following do you think is closest to the

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Which of the following do you think is closest to the temperature at 5:15am ? A = 2 . 5 o F B = 52 o F C = 43 . 5 o F D = 44 . 5 o F E = 5 . 15 o F (8.6) Tangent Line Approximation At 5am the temperature is 42 o F and increasing at a rate of 10 o F per hour. Which of the following do you think is closest to the temperature at 5:15am ? A = 2 . 5 o F B = 52 o F C = 43 . 5 o F D = 44 . 5 o F E = 5 . 15 o F D 5:15 is 1 / 4 of an hour after 5am. Temperature rises approximately (1 / 4) × 10 = 2 . 5 o F in this time. So final temperature is approximately 42 + 2 . 5 = 44 . 5 o F . Approximately because instantaneous rate of change is 10 at 5 am but this may change. Maybe by 5:10am temperature is increasing at a rate of 11 o F per hour. Answer is (initial temperature) + (rise in temperature) (rise in temperature) (time taken) × (rate of change) rate of change = derivative f (5)= 10 change input Δ x output changes 10 Δ x #### You've reached the end of your free preview.

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• Fall '07
• Wei
• Math, Derivative, sea level, plausible value
• • •  