Throughout most of calculus, I have used the method of deductive reasoning to understand new concepts . This is because it is much easier for me to understand any specific type of proof or theorem by looking at strict definitions and formulas rather than doing explorations and learning through simpler geometry. however, after being introduced to material by formulas it did help solidify it by using the simple explorations. Specifically when doing the fundamental theorem of calculus exploration I was able to use deductive reasoning throughout the worksheet to complete it and then use inductive reasoning to understand the whole theorem. The best of both worlds right? The word fundamental is defined as forming a necessary base or core. Most of calculus application and fundamental analysis is based of the use of derivatives right? Well what a coincidence! There is a theorem that specifically explains that there is a derivative and anti-derivative for any function. This seems pretty "fundamental" to any application of a derivative. Do you know what the best part of the theorem is? It ties directly into what we are learning about in class this chapter. Integrals. Through analytically analyzing of an integral, one is able to find that the integrand is actually f'(x) of an original function f(x). This is what the whole theorem implies. That there is a derivative and anti-derivative to any function! Go math.
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