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Question
If the function f(x) = 2x2 − kx + 5 is increasing on [1, 2], then k lies in the interval
Options
(−∞, 4)
(4, ∞)
(−∞, 8)
(8, ∞)
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Solution
(−∞, 4)
\[f\left( x \right) = 2 x^2 - kx + 5\]
\[f'\left( x \right) = 4x - k\]
\[\text { Forf(x) to be increasing, we must have }\]
\[f'\left( x \right) > 0\]
\[ \Rightarrow 4x - k > 0\]
\[ \Rightarrow k < 4x\]
\[\text { Since x } \in \left[ 1, 2 \right], 4x \in \left[ 4, 8 \right] . \]
\[\text { So, the minimum value of 4 x is 4 }.\]
\[\text { Since k < 4x, k < 4 }. \]
\[ \Rightarrow k \in \left( - \infty , 4 \right)\]
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