1.The sum of two numbers is 34. a) Find the largest possible product of such num

Question

1.The sum of two numbers is 34.
a) Find the largest possible product of such numbers.
b) What would be the largest possible product if the sum of the two numbers were k?
2.Sixty meters of fencing are to be used to enclose a rectangular garden.
a) Find the dimensions that will give the maximum area.
b) What would be the maximum area if k feet of fencing were used?
3.Forty feet of fencing are to enclose three sides of a rectangular patio. The fourth side
of the patio is a side of the house, and requires no fencing.
a) Find the maximum area of the patio.
b) What would be the maximum area if k feet of fencing were used?
4. A grasshopper is h(t) = 8t - 4t2 inches above the ground t seconds after it jumps.
a) How high does the grasshopper jump?
b) How long is the grasshopper in the air?
c) What relation does your answers to (a) and (b) have to the domain and the range of h?

Explanation / Answer

1. a) a+b=34 a*b=max a=34-b (34-b)*b=max max=34b-b^2 max'=34-2b 2(17-b)=max' max' is 0 for max value so 2(17-b)=0 b=17 a+b=34 so a+17=34 so a=17 so 17*17= 289

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