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In which one of the following intervals is the function $\mathrm{f}(\mathrm{x})=\mathrm{x}^{2}-5 \mathrm{x}+6$ decreasing?
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Verified Answer
The correct answer is:
$(-\infty, 2]$
$\Rightarrow f^{\prime}(x)=x^{2}-5 x+6$
$\Rightarrow \quad f^{\prime}(x) < 0$
$\Rightarrow \quad 2 x-5 < 0$
$\Rightarrow \quad x < \frac{5}{2}$
Hence, $f(x)$ is decreasing in $(-\infty, 2.5]$
$\Rightarrow \quad f^{\prime}(x) < 0$
$\Rightarrow \quad 2 x-5 < 0$
$\Rightarrow \quad x < \frac{5}{2}$
Hence, $f(x)$ is decreasing in $(-\infty, 2.5]$
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