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JEE Main & Advanced Mathematics Applications of Derivatives Question Bank Self Evaluation Test - Application of Derivatives

  • question_answer
    Let \[f(x)\] be a function defined as follows: \[f(x)=\sin ({{x}^{2}}-3x),x\le 0;\] and \[6x+5{{x}^{2}},x>0\] Then at \[x=0,f(x)\]

    A) Has a local maximum

    B)

    C) Is discontinuous

    D) None of these

    Correct Answer: B

    Solution :

    [b] \[f(0)=\sin 0=0,f({{0}^{+}})\to {{0}^{+}}\] \[f({{0}^{-}})=\underset{x\to {{0}^{-}}}{\mathop{\lim }}\,\sin ({{x}^{2}}-3x)=\underset{h\to 0}{\mathop{\lim }}\,\sin ({{h}^{2}}+3h)\to {{0}^{+}}\] Thus, \[f({{0}^{+}})>f(0)\] and \[f({{0}^{-}})>f(0)\]. Hence, \[x=0\] is a point of minima. Has a local minimum


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