Application of DerivativeHard
Question
Let f(x) = xm/n for x ∈ R where m and n are integers, m even and n odd and 0 < m < n. Then
Options
A.f(x) decreases on (- ∞, 0]
B.f(x) increases on [0, ¥)
C.f(x) increases on (- ∞, 0]
D.f(x) decreases on [0, ∞)
Solution
f′(x) = 
m - n is odd.
f′(x) < 0 ∀ x ∈ (- ∞, 0)
f′(x) > 0 ∀ x ∈ (0, ∞)
m - n is odd.
f′(x) < 0 ∀ x ∈ (- ∞, 0)
f′(x) > 0 ∀ x ∈ (0, ∞)
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