Question 27: Which of the following functions has only a maximum but no minimum?

A. \(y=-10 x^{4}-5 x^{2}+7\)

B. \(y=-17 x^{3}+2 x^{2}+x+5\)

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

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

Consider the function \(y=-10 x^{4}-5 x^{2}+7 \text { yes } y^{\prime}=-40 x^{3}-10 x=0 \Leftrightarrow x=0\ )

\(y”=-120x^2-10, y^{\prime \prime}(0)=-10<0\) so the function reaches its maximum at x = 0 .

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