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question mark

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

shefali sharma , 14 Years ago

Grade 12

1 Answers

Jitender Singh

Last Activity: 10 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

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