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if the function f(x)=2x^2-kx+5 is increased on [1,2],then k lies in interval ________

if the function f(x)=2x^2-kx+5 is increased on [1,2],then k lies in interval ________

Grade:12

1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
6 years ago
Ans:
If f(x) is increasing in [1,2], then f(x) > 0 in the interval
f(x)= 2x^{2}-kx+5
f^{'}(x)= 4x-k > 0
4-k > 0
8-k > 0
\Rightarrow k< 4
\Delta \geq 0
k^{2}-4.2.5\geq 0
(k-\sqrt{40})(k+\sqrt{40})\geq 0
\Rightarrow k\geq \sqrt{40}, k\leq -\sqrt{40}
\Rightarrow k\leq -\sqrt{40}
Thanks & Regards
Jitender Singh
IIT Delhi
askIITians Faculty

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