Question 28: Which of the following functions has a maximum at (x=frac{3}{2} ?)

Question 28: Which of the following functions has a maximum at \(x=\frac{3}{2} ?\)

A. \(y=\frac{1}{2} x^{4}-x^{3}+x^{2}-3 x\)

B. \(y=\sqrt{-x^{2}+3 x-2}\)

C. \(y=\sqrt{4 x^{2}-12 x-8}\)

D. \(y=\frac{x-1}{x+2}\)

Consider the function with \(y=\sqrt{-x^{2}+3 x-2} \text { yes } y^{\prime}=\frac{-2 x+3}{2 \sqrt{-x^{2 }+3 x-2}}\)

\(y’=0\Leftrightarrow x=\frac{3}{2}\)

The variation table sees y’ change sign from “
+” to ” -” when \(x=\frac{3}{2}\) so the function reaches its maximum at \(x=\frac{3}{2}\)

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