Question about derivatives and continuous

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SUMMARY

Every continuous function is a derivative of some indefinite integral of itself, as established by the Fundamental Theorem of Calculus. This theorem asserts that all continuous functions are integrable, which directly links continuity to the existence of derivatives. While not every derivative is continuous, the continuity of a function guarantees that it can be represented as a derivative. Understanding this relationship is crucial for grasping the foundational concepts of calculus.

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  • Basic knowledge of continuous functions
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kala
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Why is it that every continuous function is a derivative?
I know that not every derivative is continuous, I just don't know really know why we would know that every continuous function is a derivative. I think is has something to do with the integral, but I don't know how. Any help?
 
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Fundamental Theorem of Calculus
 
Specifically, every continuous function is integrable, so it is the derivative of some indefinite integral of itself.
 

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