Increasing and Decreasing Functions Relative Maxima and Relative
- Slides: 23
§ § Increasing and Decreasing Functions Relative Maxima and Relative Minima Even and Odd Functions and Symmetry Functions and Difference Quotients
State the intervals on which the given function is increasing, decreasing, and constant. Constant: none Go from left to right like you’re walking a trail. Remember to use x-coordinates.
Constant: none Go from left to right like you’re walking a trail. Remember to use x-coordinates.
* (Also known as local maxima and local minima) Keep it simple. Look for the points at which the function changes its increasing or decreasing behavior. These are the turning points.
Where are the relative maxima? Where are the relative minima?
* The function passes through the origin. The left and right sides of the graph are reflections of each other. Notice that the y-coordinate stays the same.
The alternate opposite sides show symmetry to each other. The function passes through the origin.
It is an even function. It passes through the origin. It is symmetrical on both sides of the y-axis.
The function is odd. It passes through the origin. The alternate opposite sides show symmetry to each other.
EVEN FUNCTIONS Algebraically: f(-x) = f(x) for all x in the domain of f. This means you take the function and plug in –x for x. If you end up with the original equation, it is an even function or symmetric with respect to the y-axis.
ODD FUNCTIONS Algebraically: f(-x) = -f(x) for all x in the domain of f. This means you take the function and plug in – x for x. If you end up with the opposite of the original equation – it is an odd function or symmetric with respect to the origin.
Verifying Algebraically….
Odd Even Neither
The Difference Quotient The difference quotient of a function f is an expression of the form where h ≠ 0. Where does it come from? The difference quotient, allows you to find the slope of any curve or line at any single point.
Steps Used in Finding A Difference Quotient
- Aims and objectives of increasing and decreasing functions
- Lesson 4 increasing and decreasing functions
- Lesson 5 increasing and decreasing functions
- Strictly increasing and decreasing functions
- Intervals of increasing and decreasing
- Increasing decreasing and piecewise functions
- Local maximum and minimum vs. absolute maximum and minimum
- Difference between fresnel and fraunhofer diffraction
- Factual information meaning
- How to find increasing and decreasing intervals on a graph
- Increasing intervals
- Increasing decreasing constant
- Increasing and decreasing recipes
- Interval of increase and decrease parabola
- Explain pictures
- Increasing at a decreasing rate
- Relative maxima
- Relative vs absolute max and min
- Maxima and minima
- Sulfur decaselenide
- Elements in order of decreasing electronegativity
- How to find percent decrease
- Decreasing metallic character
- First fit decreasing bin packing