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KVPY Sample Paper KVPY Stream-SX Model Paper-14

  • question_answer
    If f and g are differentiable functions in [0, 1] satisfying. \[f(0)=2=g(0)\] and\[f(1)=6,\]then for some \[c\in ]\,0,1\,[:\]

    A) \[2f'(c)=g'(c)\]

    B) \[2f'(c)=3g'(c)\]

    C) \[f'(c)=g'(c)\]

    D) \[f'(c)=2g'(c)\]

    Correct Answer: D

    Solution :

    Let        \[h(f)=f(x)-2g(x)\] as         \[h(0)=h(1)=2\] Hence, using Rolle?s  theorem             \[h'(c)=0\] \[\Rightarrow \]   \[f\,'(c)=2g'(c)\]


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