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Rate of Change Calculator

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Example
Created on 2024-06-20Asked by Mila Mitchell (Solvelet student)
Find the average rate of change of the function f(x)=x2+3x+2 f(x) = x^2 + 3x + 2 from x=1 x = 1 to x=4 x = 4 .

Solution

To find the average rate of change of the function f(x)=x2+3x+2 f(x) = x^2 + 3x + 2 from x=1 x = 1 to x=4 x = 4 : 1. **Calculate f(1) f(1) and f(4) f(4) :** f(1)=12+3(1)+2=1+3+2=6. f(1) = 1^2 + 3(1) + 2 = 1 + 3 + 2 = 6. f(4)=42+3(4)+2=16+12+2=30. f(4) = 4^2 + 3(4) + 2 = 16 + 12 + 2 = 30. 2. **Use the formula for the average rate of change:** Average rate of change=f(4)−f(1)4−1. \text{Average rate of change} = \frac{f(4) - f(1)}{4 - 1}. 3. **Substitute the values:** Average rate of change=30−64−1=243=8. \text{Average rate of change} = \frac{30 - 6}{4 - 1} = \frac{24}{3} = 8. Therefore, the average rate of change of the function from x=1 x = 1 to x=4 x = 4 is 8. Solved on Solvelet with Basic AI Model
Some of the related questions asked by Ethan White on Solvelet
1. Find the average rate of change of the function f(x)=2x2−3x+1 f(x) = 2x^2 - 3x + 1 over the interval [1,3] [1, 3] .2. Determine the instantaneous rate of change of the function g(t)=4t3−6t2+2t g(t) = 4t^3 - 6t^2 + 2t at t=2 t = 2 .
DefinitionIn calculus, this is described by its derivative, which denotes immediate rate of change of a function. For instance, the velocity of an object d dt s(t) d t s ( t ) is, by definition, the rate of change of its position with respect to time, or, mathematically, v(t) = d dt s(t).
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