Just a quickish question I wanted to ask you Zacken I have been working on differentiation and integration and I was wondering if you could just explain what the findings and numbers actually mean.
One in particular I was just doing and whilst I got the question right I just wasn't sure how to interpret that into English if you will...Question:On a car journey, the average speed of a car is v m/s-1. For v greater or equal to 5, the cost per km, C pence, of the journey is modelled by
C = 160/V + V^2/100
Using this model,
a) Show, by calculus, that there is a value of v for which C has a stationary value, and find this value of v.So I have differentiated it and got V = 20 What does this actually mean in terms of C??
b) Justify that this value of v gives a minimum value.I got the second derivative and proved that it was in fact a minimum value of C - what is this showing me exactly...???
c) Find the minimum value of C and hence find the minimum cost of a 250 km car journey.
So - I put my minimum value of v which is 20 back into the original equation and got 12 - what does this show me? I did have to look at the answers at this point because I wasn't sure what to do with my 12 - turns out I had to multiply it by 250 to get 3000 so the cost was £30
So like I said I know how to do the questions, for the most part, but just not sure what all those numbers actually mean in a real life situation. I think they should do more questions like this instead of just using graphs all the time because you can't really relate to graphs.
Anyway, if you have the time I would appreciate it any help and teaching you can offer!