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Home » Mathematics » High School Basics (Ages 12-16)
 
Maximum of Exponential Difference, Part 2
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Arrange your tan
Riemann Hypothesis
Riemann Hypothesis

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#1
Maximum of Exponential Difference, Part 2
my problem
Let k = a real number greater than 1.

Given y = k^x - (k^2)^x, what is the maximum value of the function?

PostPosted: Wed Nov 04, 2009 9:13 am  Back to top 
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Dr Sonnhard Graubner
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Birch & Swinnerton Dyer

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#2
hello, setting k^x=t so we get
f\left(\frac{\ln(t)}{\ln(k)}\right)=-\left(t-\frac{1}{2}\right)^2+\frac{1}{4}\le\frac{1}{4}
the maximum will be obtained for x=-\frac{\ln(2)}{\ln(k)}.
Sonnhard.

PostPosted: Wed Nov 04, 2009 9:33 am  Back to top 
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