Hypotheses of Calc 1 Theorems
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Theorems of Differential Calculus
This example demonstrates the hypothesis conditions and geometric interpretations of several important theorems in Calculus 1. It involves core math concepts like functions, trigonometric functions, power functions, right triangles, and correlation. Constructed using GeoGebra commands/objects such as f, g, h, A, B, C, D, p, E. Suitable for first-year university students or those reviewing calculus fundamentals.
GeoGebra Commands & Parameters
f(x) = If[-1 < x < 2, abs(x)]g(x) = If[2 < x < 5, (x - 3)^(2) + 1]h(x) = If[x > 5, 1 / (x - 5)](2, 2)(5, 5)(-1, 1)(-1, 3)p(x) = If[x < -1, 3](-1, 1)
AI Drawing Prompt Reference
In a single coordinate plane, draw three piecewise function graphs. First plot f(x)=|x| for -1<x<2, including the boundary points (-1,1) and (2,2). Next plot g(x)=(x-3)^2+1 for 2<x<5, showing its connection from (2,2) up to the point (5,5). Then plot h(x)=1/(x-5) for x>5, continuing from (5,5). Finally, mark the additional points (-1,3) and (-1,1) near the left boundary to support the geometric interpretation of the hypotheses.
The prompt above was compiled from the original drawing commands and is for reference only.