Polynomial Functions and Rates of Change
Alice White
7 min read
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Study Guide Overview
This study guide covers polynomial functions, including a refresher on their definition and key terms like degree and leading coefficient. It explores minima and maxima, both local and global, and how to find zeros of polynomials. The guide also discusses inflection points and concavity. Even degree polynomials and their properties are highlighted. Finally, it provides practice questions covering these concepts and offers exam tips.
#1.4 Polynomial Functions and Rates of Change
# 🤓 A Refresher on Polynomial Functions
Hey there! Let's quickly revisit polynomial functions. You've definitely seen these before. Think of them as the workhorses of math, showing up everywhere!
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Polynomial functions are basically sums of terms, where each term is a constant times a variable raised to a non-negative integer power.
A polynomial function is expressed as , where 'n' is a non-negative integer, and the 'a' values are real numbers. The degree of the polynomial is the highest power of the variable (n).
Remember that a constant function (like ) is also a polynomial, but its degree is zero.
# 📊 Minima and Maxima
Polynomial functions change direction as you move along their graph. These "switching points" are where the function hits a local maximum (peak) or a local minimum (valley). Think of them as the high and low points in a specific region of the graph. ⛰️
Sometimes, a polynomial might only be defined over a specific interval (restricted domain). In that case, the endpoints of the interval can also be local maxima or minima.
The global maximum is the absolute highest point of the entire graph, and the global minimum is the absolute lowest point. 🌐
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