Asked by David
The graph of f (x) = RootIndex 3 StartRoot x + 8 EndRoot is shown.
On a coordinate plane, a cube root function goes through (negative 16, negative 2), has an inflectio point at (negative 8, 0), and goes through (0, 2).
Which statement is true?
The function is only increasing when x ≥ −8.
The function is always increasing.
A or B
All Answers 1
Answered by
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B — the function is always increasing.
Reason: f(x) = ∛(x+8) is a shifted cube-root, which is strictly increasing for all real x. Its derivative f'(x) = 1/(3(x+8)^{2/3}) is positive for every x ≠ −8 (and the function increases through x = −8 as well), so f increases everywhere.
Reason: f(x) = ∛(x+8) is a shifted cube-root, which is strictly increasing for all real x. Its derivative f'(x) = 1/(3(x+8)^{2/3}) is positive for every x ≠ −8 (and the function increases through x = −8 as well), so f increases everywhere.
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