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a. no relative extrema; inflection point at x=8e^-7/12 b. relative maximum at x=

ID: 2841141 • Letter: A

Question


a.

no relative extrema; inflection point at x=8e^-7/12


b.

relative maximum at x=(8/e)^1/4 ; inflection point at x=8e^-1/4


c.

relative minimum at x=8e^1/4 ; inflection point at x=8e^-7/12


d.

no relative extrema; inflection point at x=8e^-7/12


e.

relative minimum at x=(8/e)^1/4 ; no inflection points


a.

no relative extrema; inflection point at x=8e^-7/12


b.

relative maximum at x=(8/e)^1/4 ; inflection point at x=8e^-1/4


c.

relative minimum at x=8e^1/4 ; inflection point at x=8e^-7/12


d.

no relative extrema; inflection point at x=8e^-7/12


e.

relative minimum at x=(8/e)^1/4 ; no inflection points

Explanation / Answer

Relative extrema possibly occur when the derivative is zero (or non-existent), but simplify the function first.
F(x) = 4xln|x|/8 = (1/2)xln|x|
F'(x) = (1/2)ln|x| + (x/2)(sgn(x)/|x|) = (1/2)ln|x| + (1/2) = 0 <-- product rule
ln|x| + 1 = 0
ln|x| = -1
|x| = exp(-1)
x =