Rate Of Change Flashcards
How do you determine the average rate of change between two points on a function?
Find the difference in y-values divided by the difference in x-values (f(b) - f(a)) / (b - a)
What is the formula for estimating the instantaneous rate of change at a point?
Use the average rate of change over a small interval around the point
How do you determine the instantaneous rate of change at a point on a curve?
Find the derivative of the function at that point or use the slope of the tangent line
What does the slope of a distance-time graph represent?
It represents the speed or velocity
How do you determine if a value is a maximum based on the instantaneous rate of change?
If the instantaneous rate of change changes from positive to negative, it’s a maximum
How do you determine if a value is a minimum based on the instantaneous rate of change?
If the instantaneous rate of change changes from negative to positive, it’s a minimum
What does the area under a speed-time graph represent?
It represents the distance traveled
How can you use rates of change to create a graphical model?
Plot the points of the function and use the slope between intervals to estimate the curve
If a distance-time graph is a straight line, what does that indicate?
It indicates constant speed
If a speed-time graph is a straight horizontal line, what does that indicate?
It indicates constant speed or velocity
How do you solve a word problem involving the rate of change of a population?
Find the difference in population over time and divide by the time interval
What is the meaning of a zero slope on a distance-time graph?
The object is stationary
How do you interpret a steep slope on a distance-time graph?
A steep slope indicates a high speed or velocity
What is the difference between average rate of change and instantaneous rate of change?
Average rate of change is over an interval, while instantaneous rate of change is at a specific point
If the instantaneous rate of change is positive, what does it mean about the function?
The function is increasing at that point
If the instantaneous rate of change is negative, what does it mean about the function?
The function is decreasing at that point
How do you find the slope of the tangent line to a curve at a specific point?
Find the derivative of the function and substitute the x-value of the point
What does a negative slope on a speed-time graph indicate?
It indicates deceleration
How can you estimate the instantaneous rate of change from a table of values?
Calculate the average rate of change over very small intervals around the point
How do you solve a word problem involving the rate of change of a car’s speed?
Find the change in speed over time and divide by the time interval
What does it mean if the instantaneous rate of change at a point is zero?
The point could be a local maximum, minimum, or a point of inflection
How do you find the average rate of change from a distance-time graph?
Calculate the total distance traveled divided by the total time
How do you interpret a curved distance-time graph?
It indicates changing speed or acceleration
If a function has a constant rate of change, what type of function is it?
A linear function
What is the relationship between velocity and the rate of change in a distance-time graph?
Velocity is the rate of change of distance with respect to time
