Euclid's Muse

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Search Results for “Theorem”

By Irina Lyublinskaya
Exploring Rolle's Theorem
Explore conditions of the Rolle's Theorem. The applet shows the graph of continuous differentiable function f(x) on a closed interval  [a, b]. Case 1.  f(x) < f(a) for some x inside the interval (a, b). Can you find the number c such that f'(c)=0? What did you notice about the point when f'(c)=0? Case 2.  f(x) > f(a) for some x inside the interval (a, b). Can you find the number  c such that f'(c)=0? What did you notice about the point when f'(c)=0? Can a given function have more than one number on a given interval such that f'(c)=0?

Tags: Calclulus

By Irina Lyublinskaya
Application of The Mean Value Theorem to problem solving
If f(2) = -2 and f'(x) >=2 for 2<=x<=6, how small can f(6) possibly be?

Tags: calculus

By Irina Lyublinskaya
Application of The Mean Value Theorem to problem solving
Given function f(x) = arctan (1-x) on the interval [0, 1].

Tags: calculus

By Aidan Wenzel
Sliding Ladder Problem
One of the first calculus class problems is the sliding ladder. In this problem, a ladder is resting against a wall when, all of a sudden, it starts sliding down! In this problem you're solving for dx/dt or the rate at which the point B is moving away from the wall (point C). Input constraints: -The rate of slide must be negative for the ladder to slide down -The initial height of the ladder must be less than the ladders length

Tags: Ladder, Calculus, Derivatives, Pythagorean-Theorem

By Phil Todd
Euclid 1:47
Euclid's proof of the Pythagorean Theorem is illustrated.

Tags: Pythagoras, Pythagorean, Euclid


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