Tricky Graphics: Derivative at x=0

① This example demonstrates a cleverly designed function graph that explores the derivative (tangent slope) at x=0, highlighting potential special cases such as non-differentiability or discontinuous derivative. ② Core mathematical concepts include the geometric meaning of derivatives, limit ideas in differential calculus, and the criterion for differentiability at a point; it also touches on Poisson distribution, linear functions, and linear equations as background, but the main focus is on derivatives. ③ Construction highlights: Based on the summary, GeoGebra objects f, g, f', and g' are used to plot the original functions and their derivatives, comparing the tangent slope behavior at x=0, possibly with sliders or dynamic animations to observe changes under different parameters. ④ Suitable for senior high school or early university students learning calculus, useful for understanding boundary cases of derivative definitions, and as a classroom demonstration to clarify common misconceptions like 'differentiable implies continuous'.