Problem 38
Question
What is the average rate of change of a function?
Step-by-Step Solution
Verified Answer
The average rate of change of a function is calculated as the change in the function's output over the change in the input, usually expressed as \(\frac{f(b) - f(a)}{b-a}\)
1Step 1: Understand the Concept
The average rate of change of a function is given by the ratio of the change in the output value to the change in the input value. This can be calculated using the formula: \[Average \ Rate \ of \ Change = \frac{f(b) - f(a)}{b-a}\] where \(f\) is the function, \(a\) and \(b\) are the input values.
2Step 2: Substitute the Values
Substitute the values of \(a\), \(b\), \(f(a)\), and \(f(b)\) in the above formula. It is important to note that \(a\) and \(b\) are the x-values of two points on the function, and \(f(a)\) and \(f(b)\) are the respective y-values of these two points.
3Step 3: Compute
After substituting values, execute the arithmetic operations to get the average rate of the function.
Other exercises in this chapter
Problem 38
Write the standard form of the equation of the circle with the given center and radius. Center \((-5,-3), r=\sqrt{5}\)
View solution Problem 38
Let \(P(x, y)\) be a point on the graph of \(y=\sqrt{x} .\) Express the distance, \(d,\) from \(P\) to (2,0) as a function of the point's \(x\) -coordinate.
View solution Problem 38
Determine whether each function is even, odd, or neither. Then determine whether the function's graph is symmetric with respect to the \(y\) -axis, the origin,
View solution Problem 38
Find \(f+g, f-g,\) fg, and \(\frac{f}{x}\). Determine the domain for each function. $$f(x)=5-x^{2}, g(x)=x^{2}+4 x-12$$
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