Let f:[0,1]\(\rightarrow\)R be a function. suppose the function f is twice differentiable,f(0)=0=f(1) and satisfies f''(x)-2f'(x)+f(x)\(\geq\)ex,x\(\in\)[0,1], which of the following is true?
Let f:[0,1]\(\rightarrow\)R be a function. suppose the function f is twice differentiable,f(0)=0=f(1) and satisfies f''(x)-2f'(x)+f(x)\(\geq\)ex,x\(\in\)[0,1], which of the following is true?
0<f(x)<\(\infty\)
\(-\frac{1}{2}<f(x)<\frac{1}{2}\)
\(-\frac{1}{4}<f(x)<1\)
\(-\infty<f(x)<0\)
The Correct Option is D
Solution and Explanation
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Let $\left\lfloor t \right\rfloor$ be the greatest integer less than or equal to $t$. Then the least value of $p \in \mathbb{N}$ for which
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