Geometrical Applications Calculus HELP (1 Viewer)

[kayven]

The cost 'c' (in dollars per hour) of running a boat depends on the speed v(km/h) of the boat according to the formula: C=500+40v+5v^2 on a trip of 100km from port A to port B, what speed will minimise the total cost of the trip?

How should i approach a question like this?
Show all working please.
Thank you so much.

 

[airblitz7]

Differentiate C, solve C' for zero, sub the zero of C' in C'' to test the value, sub back into C to find the minimum speed.

 

[asianese]

I don't think it works because if you differentiate C, dC/dx = 40+10v...solving for dC/dx = 0. 40+10v = 0, 10v=-40, v=-4m/s negative speeds not allowed??