Largest f(1) with Differential Inequality

1800SpecialistCalculusDifferential Equations

Harvard-MIT Math Tournament

Suppose $f$ is a differentiable real function such that $f(x) + f'(x) \leq 1$ for all $x$, and $f(0) = 0$. What is the largest possible value of $f(1)$? (Hint: consider the function $e^{x} f(x)$.)

0 students attempted0% solvedRating 1800

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Largest f(1) with Differential Inequality

1800SpecialistCalculusDifferential Equations

Harvard-MIT Math Tournament

Suppose $f$ is a differentiable real function such that $f(x) + f'(x) \leq 1$ for all $x$, and $f(0) = 0$. What is the largest possible value of $f(1)$? (Hint: consider the function $e^{x} f(x)$.)

0 students attempted0% solvedRating 1800