Water coming out of a fountain is modeled by the function F(X) = -X to the power of 2+ 8X plus to wear f(X)represents the height and feet of the water from the fountain at different times X and seconds what does the average rate of change F(X) from X equals one to ask equals four represent
geez - ever think of using actual algebra? Either your typing or your dictation is really bad.
f(x) = -x^2 + 8x + "to wear"
you want the average rate of change of f(x) for 1 ≤ x ≤ 4
As usual, that is
(f(4)-f(1)) / (4-1)
so plug in your numbers.
Having been exposed to many students of this era that can no longer speak or spell properly, let me guess that by
"F(X) = -X to the power of 2+ 8X plus to wear f(X)represents the height and feet of the water"
Parker means:
F(x) = -x^2 + 8x + 2, where f(x)represents the height of the water"
Still have no idea what the "feet of the water" have to do with it.
To find the average rate of change of F(X) from X = 1 to X = 4, we need to calculate the difference in the function values divided by the difference in time.
Step 1: Substituting the given values into the function, we find:
F(1) = -(1)^2 + 8(1) + 2 = -1 + 8 + 2 = 9
F(4) = -(4)^2 + 8(4) + 2 = -16 + 32 + 2 = 18
Step 2: Calculate the difference in function values:
ΔF = F(4) - F(1) = 18 - 9 = 9
Step 3: Calculate the difference in time:
ΔX = 4 - 1 = 3
Step 4: Calculate the average rate of change:
Average rate of change = ΔF / ΔX = 9 / 3 = 3
Therefore, the average rate of change of F(X) from X = 1 to X = 4 represents a change of 3 units of height per unit of time.