On 10/29/06, Phil Henshaw <[EMAIL PROTECTED]> wrote:
Consider these 3 attributes of a company: revenue R, cost C, profit P. My simple model of a company's finances say that P = R - C. Differentiate with respect to time and get dP/dt = dR/dt - dC/dt. Assume that dR/dt at t=0 and dC/dt at t=0 are both positive. Does this imply that dP/dt >0? No; not if dR/dt < dC/dt at t=0.
So the first derivatives of the attributes of a system do not necessarily have the same sign.
Robert
Robert,
<snip>
Where the implication that things beginning from scratch have to display
implied derivatives of the same sign comes from is a corollary of the
conservation laws.
<snip>
Consider these 3 attributes of a company: revenue R, cost C, profit P. My simple model of a company's finances say that P = R - C. Differentiate with respect to time and get dP/dt = dR/dt - dC/dt. Assume that dR/dt at t=0 and dC/dt at t=0 are both positive. Does this imply that dP/dt >0? No; not if dR/dt < dC/dt at t=0.
So the first derivatives of the attributes of a system do not necessarily have the same sign.
Robert
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