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Question
If the function f(x) = x2 − kx + 5 is increasing on [2, 4], then
Options
k ∈ (2, ∞)
k ∈ (−∞, 2)
k ∈ (4, ∞)
k ∈ (−∞, 4).
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Solution
k ∈ (−∞, 4)
\[f\left( x \right) = x^2 - kx + 5\]
\[f'\left( x \right) = 2x - k\]
\[\text { Given: f(x) is increasing on } [2, 4] . \]
\[ \Rightarrow f'\left( x \right) > 0\]
\[ \Rightarrow 2x - k > 0\]
\[ \Rightarrow k < 2x\]
\[\because x \in \left[ 2, 4 \right], \text { maximum value of k is} 4,k< 4.\]
\[ \therefore k \in \left( - \infty , 4 \right)\]
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