Draw a graph to match the description given. F(x) has a positive derivative over

Question

Draw a graph to match the description given. F(x) has a positive derivative over (-infinity,0) and (4,9) and a negative derivative over (0,4) and (9,infinity). Which of the following graphs matches the description? Sketch the following curve, indicating all relative extreme points and inflection points. A storage shed is to be built in the shape of a box with a square base. It is to have a volume of 250 cubic feet. The concrete for the base costs $3 per square foot, the material for the roof costs $7 per square foot, and the material for the sides costs S2.50 per square foot. Find the dimensions of the most economical shed. Find two numbers whose product is -36 and the sum of whose squares is a minimum.

Explanation / Answer

1) c

2) a)relative extremum points (2,-13), (-2, 19) find the derivative of function and equate it to zero to get local extremum

b)point of inflection (0,3) find second derivative and equate it to zero to get point of inflection

c)graph a from the above two sets of points the graph is A

3) let length of side of base is a and height of the box be h

therefore a2h = 250 cubicfeet

hence h = 250/a2

cost for base= a2 *3

cost of top = a2 *7

cost of sides= 4* ah* 2.5

= 10 *a* (250/a2 )

= 2500/a + a2 *3+ a2 *7

= 2500/a+ 10a2

to minimize the cost find the derivative of eqn and equate it to zero to get value of a

f(a) =   2500/a+ 10a2

f'(a) = -2500/a2 + 20a = 0

therefore a= 5feet

h= 250/25 = 10 feet

4) let two numbers be x and y

x*y =-36

f= x2+y2

= x2 + (-36/x)2

f'  = 2x - 2* 36*36/ x3

x = + or- 6

therefore y = -6 or +6

therefore one nember is 6 and another is -6

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