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Rate of Change =b−aF(b)−F(a) | |
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1−0f(1)−f(0) | 1−0g(1)−g(0) |
1−04(1)+3−(4(0)+3) | 1−021(1)2+2−(21(0)2+2) |
4 | 0.5 |
From the table above, we conclude that the function f(x) has a greater rate of change from x=0 to x=1. We can also check it graphically.
Looking at the graph, we can say that both functions have the same change in the x-coordinates, but the change in the y-coordinates is greater for the function f(x). Therefore, f(x) has a greater rate of change.
Rate of Change =b−aF(b)−F(a) | |
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3−2f(3)−f(2) | 3−2g(3)−g(2) |
3−24(3)+3−(4(2)+3) | 3−221(3)2+2−(21(2)2+2) |
4 | 2.5 |
From the table above, we conclude once more that the function f(x) has a greater rate of change from x=2 to x=3. We can also check it graphically.
Looking at the graph, we can say that both functions have the same change in x-coordinates, but the change in y-coordinates is greater for the function f(x). Therefore, f(x) has a greater rate of change.
Substitute expressions
Distribute -1
Subtract terms
Subtract fractions
ba/c=b⋅ca
a2−b2=(a+b)(a−b)
Cancel out common factors
LHS⋅2=RHS⋅2
We conclude that a must be greater than or equal to 4. Therefore, the rate of change of g(x) is greater than 4 for all x≥4.