Hey guys, I'm really having trouble getting a handle on maxima and minima problem type questions. I tend to look at the answers to figure out what to do as I can never seem to understand them. Does anyone have any tips on how to understand and complete them easier?
Maxima and minima problems (1 Viewer)
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Shadowdude
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Give us a question we can work through. Like, a question you had trouble with.
A truck is to travel 1000 kilometres at a constant speed of v km/h. When travelling at v km/h, the truck consumes fuel at the rate of [6 + v^2/50] litres per hour.
The truck company pays $1/litre for fuel and pays each of the two drivers $40 per hour whilst the truck is travelling.
i) let the total cost of fuel and the drivers' wages for the trip be C dollars. Show that C = 20v + 86000 x 1/v
ii) the truck must take no longer than 12 hours to complete the trip, and speed limits require that v is less than or equal to 100.
The truck company pays $1/litre for fuel and pays each of the two drivers $40 per hour whilst the truck is travelling.
i) let the total cost of fuel and the drivers' wages for the trip be C dollars. Show that C = 20v + 86000 x 1/v
ii) the truck must take no longer than 12 hours to complete the trip, and speed limits require that v is less than or equal to 100.
Shadowdude
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The truck travels at v (km/h).
Fuel is consumed at
(L/h). But as fuel is 1 ($/L), we know that the cost of fuel per hour is ($/h).
Pay for the drivers is 80 ($/h) - because it's 40 each.
Now, 1000 km travelled at v (km/h) is done in:
hours. (as: 
)
And:
 + (wages) = (6 + \frac{v^{2}}{50})(\frac{1000}{v}) + 80(\frac{1000}{v}))
That is, cost of fuel per hour ($/h) multiplied by the number of hours h, plus the wages per hour, multiplied by the number of hours.
Simplify and you get part 1.
And I'm not sure what they're asking for part 2?
So basically, this is like one of your year 10... rates questions - but very hard. Write down the units, and that'll really help out.
Fuel is consumed at
Pay for the drivers is 80 ($/h) - because it's 40 each.
Now, 1000 km travelled at v (km/h) is done in:
And:
That is, cost of fuel per hour ($/h) multiplied by the number of hours h, plus the wages per hour, multiplied by the number of hours.
Simplify and you get part 1.
And I'm not sure what they're asking for part 2?
So basically, this is like one of your year 10... rates questions - but very hard. Write down the units, and that'll really help out.
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Well you should do as much as practice as possible because after a while, all the questions are the 'same'. That is, they require you to do the same method, just with different values. Of course, there might be some twists but you'd just have to learn from that.
iSplicer
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+1.
tambam
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I also struggled with this topic in year 12, but I think mainly it came down to silly errors or not reading the question properly.
Once you look at the solution do you understand how to do the questions? If its a matter of not being able to apply your knowledge to different scenarios, just sit down and do all the past hsc questions for this topic . You might struggle and have to 'cheat' initially, but with 2unit maths, often practice makes perfect.
If you just don't understand the topic, get your teacher or tutor to explain it to you until it clicks.