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please solve rd sharma class 12 chapter 16 Increasing and Decreasing Functions exercise Multiple choice question , question 5 maths textbook solution

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Correct option (a)

Hint: If f(x)  is increasing function {f}'(x)>0

Given:f(x)=2 x^{2}-k x+5

Explanation: It is given that

f(x)=2 x^{2}-k x+5 

Differentiate w.r.t  x

f^{\prime}(x)=2.2 x-k

\because If f(x)  is increasing function {f}'(x)>0

\begin{aligned} &\therefore 4 x-k>0 \text { on }[1,2] \\ &k<4 x \end{aligned}

So, the minimum value of k is 4x

k<4\\ \therefore k\epsilon \left ( -\infty, 4 \right )

Thus k lies in the interval \left ( -\infty ,4 \right )

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