February 21, 2017

Homework Help: calculus

Posted by Becky on Monday, August 13, 2012 at 12:56pm.

A ship uses $( 7v^2 ) of fuel per hour when travelling at a constant speed of v km/h. Other expenses in operating the ship (i.e. crew and equipment) amount to $345 per hour. The ship makes a journey of 100 km.

C(v) : (700v^2 + 34500)/v
C'(v): (700v^2 - 34500)/v^2
C"(v): 69000/v^3

Question: To minimize the total cost of the journey the ship should travel at a speed of _____km/h
Correct to 3 significant figures.

(The speed that minimizes the total cost that have calculated correspond to a zero of the derivative of the total cost. The minimum of the total cost will (for this problem) occur at a turning point of the total cost function)


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