Dr. J's Maths.com
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Calculus - Differentiation - Applied max/min questions.
Type 5: Rates - Test Yourself 2 - Solutions.


 

Time.

1.

(i) Tracey starts driving 40 km from Birdsville and travels at 1.2 km/min for t minutes. Hence she travels 1.2t km from her starting point towards the Birdsville hotel. She is therefore (40 - 1.2t) km from her destination after t minutes.

(ii) Andrew is therefore (50 - 1.5t) km from Birdsville after t minutes.

Using Pythagoras' Theorem to calculate the distance between Tracey and Andrew:

Remember.As noted on the video, we do not take the square root here as all terms would be under the root sign. Just differentiate normally. 

After 3 min 20 secs, Tracey is (40 - 1.2*3 min 20 secs) away from Birdsville - so 0 km (she has arrived!!). Use your calculator to work this out using the time/angle button.

After the same time, Andrew is (50 - 1.3*3 min 20 secs) = 0 km away (so he too has arrived)!!

So the closest distance is zero km and they had lunch together!!
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Costs.

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