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If \(-6\leq a \leq -2\) and \(3 \leq b \leq 5\), what is the greatest possible value of \(\displaystyle\left(a+\frac{1}{b}\right)\left(\frac{1}{b}-a\right) \)? Express your answer as a common fraction.

 Jun 10, 2022
 #1
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Simplifying the  given  expression we get

 

1/ b^2 - a^2

 

The first term  will be greatest when  b = 3    and the second  term will be least  when a = -2

 

So....the max  value  is

 

1/(3)^2  - (-2)^2  =   1/9  - 4 =   -35/9

 

 

cool cool cool

 Jun 10, 2022

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