Variability of Instantaneous Rate of Change
Rank the following functions by the variability of their instantaneous rate of change (i.e. the character of their second derivatives) over any interval, from least variable to most variable. The functions are: $$f(x)= 5$$ (a constant function), $$g(x)= x^2$$, $$h(x)= x^3$$, and $$k(x)= \sin(x)$$.
A
x^2, 5, sin(x), x^3
B
5, x^2, x^3, sin(x)
C
x^3, sin(x), 5, x^2
D
sin(x), x^3, x^2, 5
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