Is x = -4/3 a critical number for g(x) = (3x + 4)^3/4 ?

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Is x = -4/3 a critical number for g(x) = (3x + 4)^3/4 ?

2006-10-14 05:04:52 · 2 answers · asked by Olivia 4 in Science & Mathematics ➔ Mathematics

2 answers

g'(x) = (3/4)(3x+4)^(-1/4)*3 is undefined at x=-4/3, so yes, it is a critical point, because it's possible that g' could have opposite signs on either side of this point, making -4/3 a local maximum or minimum of g.

2006-10-14 05:12:23 · answer #1 · answered by James L 5 · 0⤊ 0⤋

g(x)=(3x+4)^3/4
g '(x)=(3/4)(3x+4)^-1/4 =0 ===> x=-4/3
g '(-4/3)=0 then this is a critical point.

2006-10-14 13:07:57 · answer #2 · answered by matchstick man 1 · 0⤊ 0⤋