Question

求值域 Y=根号下X-3+根号下15-3X

Answer 1

y=√(x-3) +√(15-3x)
x-3 ≥0 and 15-3x ≥0
x≥3 and x≤5
3≤x≤5

y=√(x-3) +√(15-3x)
y' = (1/2) [ 1/√(x-3) -3/√(15-3x) ]

y' = 0
1/√(x-3) -3/√(15-3x)=0
√(15-3x) -3√(x-3) =0
15-3x = 9x-27
12x=42
x=7/2

y'(7/2+) <0
y'(7/2-) >0
=> x= 7/2 max

max y
= y(7/2)
= √(7/2-3) +√(15-21/2)
=√(1/2) + 3√(1/2)
=2√2

y(3) = √(3-3) +√(15-9) =√6
y(5) = √(5-3) +√(15-15) =√2

值域 =[√2 , 2√2]

Answer 2

X-3>0
15-3X>0
所以3<x<5
y值域为根号下2到根号下6

Answer 3