Prove that $\int_0^1 \left| \frac{f''(x)}{f(x)} \right| dx \geq 4$, under the given conditions on $f(x)$
Suppose $f(x) \in C^2[0,1]$ such that $f(0)=f(1)=0$, and $f(x)\neq 0$ on $(0,1)$. Prove that
$$\int_0^1 \left| \frac{f''(x)}{f(x)} \right| dx \geq 4.$$
Answer
Answers can only be viewed under the following conditions:
- The questioner was satisfied with and accepted the answer, or
- The answer was evaluated as being 100% correct by the judge.
Savionf
570
The answer is accepted.
Join Matchmaticians Affiliate Marketing
Program to earn up to a 50% commission on every question that your affiliated users ask or answer.
- answered
- 489 views
- $30.00
Related Questions
- Find $\int x \sqrt{1-x}dx$
- Rank, Range, Critical Values, Preimage, and Integral of Differential Forms
- What is the asymptotic density of $A$ and $B$ which partition the reals into subsets of positive measure?
- Work problem involving pumping water from tank
- Explain parameter elimination for complex curves v2
- A Real Analysis question on convergence of functions
- Calculus Question
- Relating integrals to the area under the curve using rectangles.