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Standard XII

Mathematics

Properties of Composite Function

Let f :[0,1] ...

Question

Let f: [0, 1] →R be a function. Suppose the function f is twice differentiable, f (0) =f (1) =0 and satisfies f''(x)-2f'(x) +f(x) ≥e^x, x∈ [0, 1]. Which of the following is true for 0<x<1?

$0 < f (x) < \infty$

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\frac{- 1}{2} < f (x) < \frac{1}{2}

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$\frac{- 1}{4} < f (x) < 1$

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$- \infty < f (x) < 0$

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Solution

The correct option is D
$- \infty < f (x) < 0$

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Let f: [0, 1] →R be a function. Suppose the function f is twice differentiable, f (0) =f (1) =0 and satisfies f''(x)-2f'(x) +f(x) ≥ex, x∈ [0, 1]. Which of the following is true for 0<x<1?

The correct option is D −∞<f(x)<0

Let f: [0, 1] →R be a function. Suppose the function f is twice differentiable, f (0) =f (1) =0 and satisfies f''(x)-2f'(x) +f(x) ≥e^x, x∈ [0, 1]. Which of the following is true for 0<x<1?

The correct option is D
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