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Differential equations are mathematical equations that relate functions with their derivatives. They come in various forms and complexities. Understanding their order, degree, linearity, and homogeneity is key to classifying and solving them effectively.
The first and second derivative tests are pivotal tools in calculus for analyzing the behavior of functions. They assess where functions increase or decrease, identify local extrema, and determine concavity. While the first derivative reveals increasing or decreasing trends and locates potential extrema, the second derivative offers insights into the function’s concavity, indicating whether a […]
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