The Summer 2025 Featured Problem Series
Starting today and continuing through August 4th, iMathTutor® is running a weekly math problem series! Look for a new problem every Monday , along with the previous week's solution.
Our problems, which are derived from the courses we tutor, cover a wide range of topics, including Calculus I & II, Differential Equations, Linear Algebra, and Real Analysis.
Here is your first challenge.
Our Week 1 Problem
We thought we would ease into the series with a Penn State Math 140, i.e. Calculus I, problem. But don't be fooled, it is a bit more challenging than a typical Calc I problem, since its solution doesn't involve identifying the type of problem and applying an established algorithmic procedure.
Suppose that for some \(a < b\), \(f\) and \(g\) are continuous functions on \([a,b]\), and differentiable on \( (a,b)\). Show that if \(f(a)=g(a)\) and \(f^\prime(x)< g^\prime(x)\) on \( (a,b)\), then \(f(b) < g(b)\).