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Application of Derivatives question

2013 · Shift 2 · Q28
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  5. /2013 · Shift 2 · Q28

Application of Derivatives question

2013 · Shift 2 · Q28

JEE AdvancedMathematicsApplication of DerivativesMCQ+4 / −1
Let f:[0,1]→Rf:\left[ {0,1} \right] \to Rf:[0,1]→R(the set of all real numbers) be a function. Suppose the function fff is twice differentiable, f(0)=f(1)=0f(0) = f(1)=0f(0)=f(1)=0 and satisfies f′′(x)−2f′(x)+f(x)≥.ex,x∈[0,1]f''\left( x \right) - 2f'\left( x \right) + f\left( x \right) \ge .{e^x},x \in \left[ {0,1} \right]f′′(x)−2f′(x)+f(x)≥.ex,x∈[0,1]. Which of the following is true for 0<x<1?0 \lt x \lt 1?0<x<1?
  1. A
    0<f(x)<∞0 \lt f\left( x \right) \lt \infty0<f(x)<∞
  2. B
    −12<f(x)<12- {1 \over 2} \lt f\left( x \right) \lt {1 \over 2}−21​<f(x)<21​
  3. C
    −14<f(x)<1- {1 \over 4} \lt f\left( x \right) \lt 1−41​<f(x)<1
  4. D
    −∞<f(x)<0- \infty \lt f\left( x \right) \lt 0−∞<f(x)<0
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