MathGrit
ProblemsTechniquesPricing
Sign inGet started
Back to problems

Extrema of Integral Functional on Continuous Functions

2300ExpertCalculusFunctionsOptimization

2018 Romanian Mathematical Olympiad · 2018

Let $\mathcal{F}$ be the set of all continuous functions $f: [0, 1] \to \mathbb{R}$, satisfying $$ \max_{0 \le x \le 1} |f(x)| = 1, \text{ and let } I: \mathcal{F} \to \mathbb{R}, $$ $$ I(f) = \int_{0}^{1} f(x) \, dx - f(0) + f(1). $$
0 students attempted0% solvedRating 2300

Related practice paths

Olympiad-Style PracticeDeep contest practice for proof-style problem solving.How to Qualify for AIMEScore goals, contest choice, and prep habits for AIME hopefuls.How to Review Missed AMC ProblemsTurn missed problems into a repeatable improvement loop.

Ready to check your answer?

Create an account to submit answers, save history, and track your rating.

Progressive Hints5

Unlock hints one at a time — each reveals a little more without spoiling the solution.

Step-by-Step Solutions1

Multiple solution approaches with detailed walkthroughs, unlocked after you solve the problem.

AI-Powered Grading

Instant feedback on your answer — handles fractions, decimals, and equivalent forms.

Curated problem bank

Supported tracks for AMC, AIME, MATHCOUNTS, and olympiad-style training, plus global problem sources like UKMT, Euclid, and Kangaroo.