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I've not got a mark scheme so unsure how to do this question:

A diesel lorry is driven from Birmingham to Bury at a steady speed of v km per hour. The total cost of the journey £C is given by:

C = 1400/v + 2v/7

a) find the value of v for which C is a minimum.

This is what I'm stuck on. When it says C is minimum I thought it would be 0 as the minimum cost would be £0. So I just did 1400 + 2v = 0 and then worked out v. But it didn't work! What's v when C is 0?

A diesel lorry is driven from Birmingham to Bury at a steady speed of v km per hour. The total cost of the journey £C is given by:

C = 1400/v + 2v/7

a) find the value of v for which C is a minimum.

This is what I'm stuck on. When it says C is minimum I thought it would be 0 as the minimum cost would be £0. So I just did 1400 + 2v = 0 and then worked out v. But it didn't work! What's v when C is 0?

stanmoor

By the way, can I just ask what differentiating twice actually does?

As dy/dx is the rate of change of the y-value (and hence, dy/dx is the gradient), d²y/dx² is the rate of change of the gradient. Imagine a minimum point - the gradient on the left of it is negative, the gradient on the right of it is positive, so the gradient is increasing, meaning the rate of change of the gradient is positive (d²y/dx² > 0). Similarly, at a maximum point, the gradient gradually decreases from something positive to 0 to something negative, so d²y/dx² < 0.

generalebriety

As dy/dx is the rate of change of the y-value (and hence, dy/dx is the gradient), d²y/dx² is the rate of change of the gradient. Imagine a minimum point - the gradient on the left of it is negative, the gradient on the right of it is positive, so the gradient is increasing, meaning the rate of change of the gradient is positive (d²y/dx² > 0). Similarly, at a maximum point, the gradient gradually decreases from something positive to 0 to something negative, so d²y/dx² < 0.

But surely d^2y/dx^2 works on a certain point so how does it 'know' that the points around it are increasing?

DeathAwaitsU

But surely d^2y/dx^2 works on a certain point so how does it 'know' that the points around it are increasing?

Err...

The same way dy/dx "knows" whether the points around it are higher or lower than it. Have you seen how differentiation from first principles works?

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