Calculus: Minimum Time of Swimming and Walking

View full question and answer details: https://www.wyzant.com/resources/answ... Question: Hagrid is 3 offshore in a boat transporting some first years to Hogwarts Hagrid is 3 offshore in a boat transporting some first years to Hogwarts, located 6 down a straight shoreline from a point near the boat. He can row 2 mph and they can walk 5 mph. Where should he land the boat to reach Hogwarts in the least amount of time? ------------------------ Answered By: Shin C. K-12 Math, Calculus, and SAT Math I and II Expert More information: https://www.wyzant.com/Tutors/CA/Ranc... ------------------------ Written Explanation: We shall now find the minimum time. Apologies if there was any confusion on the video. When I said swim, I really meant to say "row".In the video, I earlier stated that the total time combined (with changing x with sqrt(u^2 + 9)) is:T = 1.2 - (u / 5) + 0.5sqrt(u^2 + 9).Remember, you can find the minimum of t by taking the derivative, and see that IF at when t'(u) = 0, t' changes from negative to positive, it's a minimum.d/du( T(u) ) = - 0.2 + u / ( 2 *sqrt(u^2 + 9) ).T ' (u) = 0 when (after algebraically solving for u) u = 6 / sqrt(21).Checking the derivative ensures that when u ‹ 6 / sqrt21, t'(u) is negative, and when u › 6 / sqrt21, t'(u) is positive. Therefore, Hagrid can land the boat at u = 6/sqrt21 miles to ensure the smallest time possible. See full answer: https://www.wyzant.com/resources/answ... ------------------------ About: Wyzant Ask an Expert offers free answers to your toughest academic and professional questions from over 80,000 verified experts. It’s trusted by millions of students each month with the majority of questions receiving an answer within 1 hour of being asked. If you ever need more than just an answer, Wyzant also offers personalized 1-on-1 sessions with experts that will work with you to help you understand whatever you’re trying to learn. Ask your own question for free: https://www.wyzant.com/resources/answ... Find a tutor for a 1-on-1 session: https://www.wyzant.com?utm_source=you... Subscribe to Wyzant on YouTube: https://www.youtube.com/subscription_...