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11th Class Mathematics Sample Paper Mathematics Olympiad - Sample Paper-5

  • question_answer
    If x is real, then the maximum value of \[\mathbf{5}+\mathbf{4x}-{{\mathbf{x}}^{\mathbf{2}}}\]is

    A) (a) 7                                         

    B) (b) 8              

    C) (c) 9                             

    D) (d) 10

    Correct Answer: C

    Solution :

    [c] \[\because y=5+4x-{{x}^{2}}\] \[\frac{dy}{dx}=4-2x\]For maximum & minimum value of y. \[\frac{dy}{dx}=0\Rightarrow 4-2x=0\] \[x=2\frac{{{d}^{2}}y}{d{{x}^{2}}}=-2\] Hence value of \[y=5+4\times 2-{{(2)}^{2}}\] \[=5+8-4=9.\]


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