5). The total cost of producing x radio sets per day is $ ( 1/4 x^2 + 35x + 25 ) and the price per set is at which they may be sold is $ ( 50 - 1/2x ). Find the daily output for maximum profit.

Answer 10 sets /day

6). The cost of fuel in running a locomotive is proportional to the square of the speed and is $25/hr for a speed of 25km/hr. The other costs are $100 /hr regardless of speed. Find the speed that will make the cost per kilometer a minimum.

Answer 50km/hr

8) A rectangular field , to enclose a given area , is fenced off along a straight river. If no fencing is needed along the river , show that the least amount of fencing will be required when the length of the field is twice the width ( this is all the info available- the condition ? length =2x width).

Solution Summary

Maximum and Minimum Values are found using derivatives.

... 3. Use the Quotient Rule to find the derivatives of the ... functions find the 1) first and second derivative, 2) explain ... or not the function has a maximum or a ...

... technique with the first and second derivative tests to ... compact set has an absolute maximum and minimum... Stationary points where the partial derivatives are zero ...

... The figure below shows the graph of the derivative of a ... of f . (b) What values of x result in a local maximum? (c) What values of x result in a local minimum? ...

... 2 1 -5 based on Chapter Partial Derivative (Maximum & Minimum... 1. Locate all relative maxima, relative minima, and ... We find the partial derivatives as follows ...

... which point the average variable cost function takes on its minimum value. ... solve for Q. Also use the second derivative to check for a maximum or minimum. ...

... file (word problems, inflection, critical points, and derivatives). ... on first derivative and second derivative of functions. ... dealing with the maximum and minimum...

Calculus Maxima, Minima and Saddle Points. ... 2. Determine derivatives (with respect to x) for the ... Determine for e. Determine the partial derivative with respect ...

... To determine whether this is a maximum or minimum we check the sign of the second derivative: ... is concave therefore the FOC finds a maximum of this ...

...maximum value at x = 6 and its value is 1 ... This posting explains how to find local maximum/minimum and tangent ... 1. Find the derivative of the function shown below ...

... solving multiple questions on the application of derivatives. ... (Apply the quotient rule carefully to find derivative.). ... 2. Find all maximum and minimum values of ...