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Determine the greatest possible value of the constant $a$.
Mathematics 9709 · AS & A Level · Differentiation
Differentiation — practice question
The function $f$ is given by $f(x) = \frac{1}{3}(2x - 1)^{\frac{3}{2}} - 2x$ for $\frac{1}{2} < x < a$. It is stated that $f$ decreases as $x$ increases.