Average Rate of Change Table Calculator
The average rate of change of a function over an interval tells us how much the function's output changes, on average, for each unit of change in the input. For a function \(f(x)\), the average rate of change over the interval \([a, b]\) is calculated as:
\[
\text{Average Rate of Change} = \frac{f(b) – f(a)}{b – a}
\]
This calculator helps you compute the average rate of change for a given function by inputting specific interval points.
function calculateAverageRateOfChange() {
var functionString = document.getElementById("functionInput").value;
var a = parseFloat(document.getElementById("startInterval").value);
var b = parseFloat(document.getElementById("endInterval").value);
var resultDiv = document.getElementById("result");
if (isNaN(a) || isNaN(b)) {
resultDiv.innerHTML = "Error: Please enter valid numbers for the interval endpoints.";
return;
}
if (a === b) {
resultDiv.innerHTML = "Error: The start and end of the interval cannot be the same.";
return;
}
if (!functionString) {
resultDiv.innerHTML = "Error: Please enter a function.";
return;
}
try {
// Function to evaluate the user-provided function string
// This is a simplified parser and might not handle all complex JS expressions.
// For a robust solution, consider a dedicated math expression parser library.
var evaluateFunction = function(x_val) {
// Basic sanitization: replace 'x' with the value, handle basic operators
// IMPORTANT: eval() is dangerous if input is not controlled.
// In a real-world scenario, use a safer parsing method.
var substitutedString = functionString.replace(/x/g, '(' + x_val + ')');
substitutedString = substitutedString.replace(/\^/g, '**'); // For exponentiation
return eval(substitutedString);
};
var fa = evaluateFunction(a);
var fb = evaluateFunction(b);
if (isNaN(fa) || isNaN(fb)) {
resultDiv.innerHTML = "Error: Could not evaluate the function at the given interval points. Check your function and input values.";
return;
}
var rateOfChange = (fb – fa) / (b – a);
resultDiv.innerHTML = "
" +
"| Interval | f(a) | f(b) | Change in x (b-a) | Change in f(x) (f(b)-f(a)) | Average Rate of Change |
|---|
" +
"" +
"| [" + a + ", " + b + "] | " +
"" + fa.toFixed(4) + " | " +
"" + fb.toFixed(4) + " | " +
"" + (b – a).toFixed(4) + " | " +
"" + (fb – fa).toFixed(4) + " | " +
"" + rateOfChange.toFixed(4) + " | " +
"
" +
"
";
} catch (error) {
resultDiv.innerHTML = "Error evaluating function: " + error.message + ". Please check your function syntax.";
}
}
.calculator-container {
font-family: sans-serif;
max-width: 600px;
margin: 20px auto;
padding: 20px;
border: 1px solid #ccc;
border-radius: 8px;
box-shadow: 0 2px 5px rgba(0,0,0,0.1);
}
.calculator-container h2 {
text-align: center;
margin-bottom: 15px;
color: #333;
}
.calculator-container p {
margin-bottom: 20px;
color: #555;
line-height: 1.6;
}
.calculator-inputs {
display: flex;
flex-wrap: wrap;
gap: 15px;
justify-content: center;
margin-bottom: 20px;
}
.input-group {
display: flex;
flex-direction: column;
min-width: 150px;
flex: 1;
}
.input-group label {
margin-bottom: 5px;
font-weight: bold;
color: #333;
}
.input-group input[type="text"] {
padding: 8px;
border: 1px solid #ccc;
border-radius: 4px;
font-size: 1em;
}
.calculator-inputs button {
padding: 10px 20px;
background-color: #007bff;
color: white;
border: none;
border-radius: 4px;
cursor: pointer;
font-size: 1em;
transition: background-color 0.3s ease;
}
.calculator-inputs button:hover {
background-color: #0056b3;
}
.calculator-result {
margin-top: 20px;
padding: 15px;
background-color: #f8f9fa;
border: 1px solid #e0e0e0;
border-radius: 4px;
overflow-x: auto; /* For tables that might be wide */
}
.calculator-result table {
width: 100%;
border-collapse: collapse;
text-align: center;
}
.calculator-result th, .calculator-result td {
padding: 10px;
border: 1px solid #ddd;
}
.calculator-result th {
background-color: #e9ecef;
font-weight: bold;
}
.calculator-result tr:nth-child(even) {
background-color: #f2f2f2;
}