Question

Two stoves are located 46 feet apart, one giving out 4 times as much heat as the other. If you stand at a point on the line between the stoves at a distance x from the less powerful stove, the temperature of the air is given by

H(x)=100 + 60/x^2 + 240/(46-x)^2 .

Assume you move back an forth between the two stoves, always at least 4 ft from either stove.

(a) Assume you wish to determine the maximum and minimum temperatures you would experience. The domain to study for the function H(X) would be: [____,_____]

(b) There is one critical number for the function on the domain in (a) and it is _______

(c) The maximum temperature you would experience is max = _______

(d) The minimum temperature you would experience is min = ______

(c) The maximum temperature you would experience is max = _______

(d) The minimum temperature you would experience is min = ______

Answer 1

Solution : Given the temperative function: 1465 H (wyaf100+'Go } for having critical numbs: 9 no g mot el mare o 46 az Goya 1. Ande f). We shall find out 190 4x = (416-733 » 44 x = 46-x3 (43+1)x=46 jº 1+(4) mal values at the Critical nunks as well as at the end points too. Af x=4: #(4) = 100+60 +34 02 = 100+ 4.0 + 60, 103.88609 Af x=42. H(42) = 100+ 0 0.0 Buod 100+ lyga the functional values a 1. . 60 100+ 60 100+ 103.88 609 49 4,2 - 100 + 15+ IS 115.034. 1 60 240 Afx= 46_ o 17.7784577 it 314 H/17.77877537) 100+ (17.77848773 (28.221542372 = 100+ 0.189829229 +0.301335122 = 100.491164351 shus: Max. = 1115.034 ] Aus. os. Min. = 1100-4911643511 Aos,