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Answer by STrick for Maximization of an expression involving exponentials
We can proceed from your idea, by setting $a=2^x$ and $b=3^x.$Then, consider the expression$$S=a^2+a^3+b^2-1-a-ab-a^2b$$which is a quadratic with respect to $b$ and the discriminant is $\Delta...
View ArticleAnswer by Theo Bendit for Maximization of an expression involving exponentials
You can compute the derivative:$$f'(x) = 4^x \ln 4 + 8^x \ln 8 + 9^x \ln 9 - 2^x \ln 2 - 6^x \ln 6 - 12^x \ln 12.$$My instinct would be that a "nice" value of $x$ will probably make $f'(x) = 0$...
View ArticleMaximization of an expression involving exponentials
The problem goes something like this:$$ f(x) = 4^x+8^x+9^x-2^x-6^x-12^x$$Find the maximum value of f(x).This question appeared on a test in which calculators were not allowed, so please refrain from...
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