Calculus Applications Math Studies 1

a)Find the local extrema and identify them as either a local maximum or a local minimum. b)Find the coordinates of the absolute maximum and absolute minimum of the function in the interval

First, differentiate. Set f(x) to 0 Solve for x Factor Hence, we have local extrema at x = 10 and x = 20

To identify them as either maxima or minima, we can use the derivative -

To identify them as either maxima or minima, we can use the derivative -

b) Check the endpoints, x = 0 and x = 30

2.A rectangular pen is to be fenced in using two types of fencing. Two opposite sides will use heavy duty fencing at $3/ft while the remaining two sides will use standard fencing at $1/ft. What are the dimensions of the rectangular plot of greatest area that can be fenced in at a total cost of $3600? 3x 1y Therefore max The dimensions of a rectangular plot of greatest area are 300 x 900

4. An open-top box with a square bottom and rectangular sides is to have a volume of 256 cubic inches. Find the dimensions that require the minimum amount of material. therefore a min 8 x 8 x 4 y x x