Y = -9/x -x ; x∈[1;4].
y(1) = -9/1 -1 = - 10.
y(4) = -9/4 -4 = -6,25.
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y '= (-9/x -x)' =9/x² -1 =(9-x²)/x²=(3+x)(3-x)/x² .
y '= 0 ⇒(x+3)(3-x)/x² =0 ⇒x₁ = -3∉ [1;4], x₂ =3.
y(3) = -9/(3) -3 = -6.
min(y) = y(1) = -10.
max(y) =y(3) = - 6.
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y =4/x +x ; x∈[1;3] .
y (1) =4/1+1 =5.
y (3) =4/3+3 =[4] 1/3.
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y '= (4/x +x)' = - 4/x² +1 =(x² -4)/x² =(x+2)(x-2)/x².
y '= 0 ⇒(x+2)(x-2)/x² =0 ⇒x₁ = -2∉ [1;3], x₂ =2.
y(2) = 4/2 +2 = 4.
min(y) = y(2) = 4.
max(y) =y(1) = 5.