Question 45: Find all real values of m so that the function \(y=x^{3}-2 x^{2}+(m+3) x-1\) has no extremes?
\(\begin{array}{l} y^{\prime}=3 x^{2}-4 x+m+3\\ \text { Function without extrema } \Leftrightarrow \Delta_{y^{ \prime}}^{\prime} \leq 0 \Leftrightarrow 4-3(m+3) \leq 0 \Leftrightarrow m \geq-\frac{5}{3} \end{array}\)
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