c2. Decreasing on interval(s): \( (-10,-4) \) c3. Constant on interval(s): d1. Coordinates of local maxima (separated by commas): d2. Coordinates of local minima (separated by commas): e. Symmetry: Neither Even f1. Find \( f(8) \) : f2. Find \( x \) when \( f(x)=3 \) : 3. \( f(1) \) Positive Negative h. Interval where \( f(x)<0 \) :
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The Deep Dive
Want to dive into some context? The study of functions and their behaviors, like increasing, decreasing, and finding maxima and minima, dates back to early days of calculus with pioneers such as Newton and Leibniz. They laid the groundwork for understanding how changes in a function can reveal crucial insights. It’s fascinating how these concepts are now essential in fields ranging from economics to engineering! When it comes to real-world applications, understanding functions can be a game-changer. For example, companies use calculus to maximize profits and minimize costs by analyzing their revenue functions. Imagine a candy factory optimizing production levels to ensure they meet demand while keeping costs low—calculating those intervals of increase and decrease can lead to sweet success!