Homework Solutions

Solutions to homework in 7.3

#8 e^-x - x e^-x

#10 (e^2x+2x)^-1/2(e^2x+1)

#38 local max: at x = 1
local min: at x = 0
increasing: [0, 1]
decreasing: (-∞, 0) ∪ (1, ∞)
inflection points: at x = 1+^√2/₂ and 1-^√2/₂
concave up: (-∞, 1-^√2/₂) ∪ (1+^√2/₂, ∞)
concave down: (1-^√2/₂, 1+^√2/₂)

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#8	e^-x - x e^-x
#10	(e^2x+2x)^-1/2(e^2x+1)
#38	local max: at x = 1 local min: at x = 0 increasing: [0, 1] decreasing: (-∞, 0) ∪ (1, ∞) inflection points: at x = 1+^√2/₂ and 1-^√2/₂ concave up: (-∞, 1-^√2/₂) ∪ (1+^√2/₂, ∞) concave down: (1-^√2/₂, 1+^√2/₂)