Pre-calculus Function QuestionDate: 2/8/96 at 14:51:2 From: Dan Belter Subject: Pre-Calc Question Our class was doing work with exponents and logarithms today, and we came across this function: f(x)=3De^(1/x) We were wondering if this function had a local minimum. Thanks, -Dan Belter Date: 8/3/96 at 9:36:22 From: Doctor Jerry Subject: Re: Pre-Calc Question I'm not certain whether D is a constant and, if so, whether it is positive or negative. Maybe it means derivative? If I assume that D is a positive constant and f is defined for all x other than 0, then 1. for small positive x, like x=0.001, f is large. 2. for large positive x, like x=1000, f is a little larger than 3D. 3. for small negative x, like x=-1000, f is a little smaller than 3D. 4. for large negative x, like x=-0.001, f is a little larger than 0. So, as x comes in from negative infinity, the graph decreases from 3D and approaches 0 as x approaches 0 from the left. Since f does not take the value 0, it has no local minimum for x<0. As x continues past 0 and becomes large, the graph just decreases from infinity towards 3D, but never take on this value. So, again, f has no local minimum (of 3D). So, f has no local minimum, unless D=0, in which case, f has a local minimum for all x not equal to 0. -Doctor Jerry, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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