find the average rate of change for the function f(x)=60x-3x^2 between x=6 and x=19
unless there is a special definition of "average rate of change" that im not aware of, ur answer is (f(19) - f(6))/(19-6)
To find the average rate of change for the function f(x) = 60x - 3x^2 between x = 6 and x = 19, we can use the formula:
Average rate of change = (f(b) - f(a)) / (b - a)
where a and b are the given x-values, and f(a) and f(b) are the corresponding function values.
In this case, a = 6 and b = 19.
Substituting these values into the formula:
Average rate of change = (f(19) - f(6)) / (19 - 6)
To find f(19), we substitute x = 19 into the function:
f(19) = 60(19) - 3(19)^2
f(19) = 1140 - 3(361)
f(19) = 1140 - 1083
f(19) = 57
Similarly, to find f(6), we substitute x = 6 into the function:
f(6) = 60(6) - 3(6)^2
f(6) = 360 - 3(36)
f(6) = 360 - 108
f(6) = 252
Now, substituting these values back into the formula:
Average rate of change = (57 - 252) / (19 - 6)
Average rate of change = (-195) / (13)
Average rate of change = -15
Therefore, the average rate of change for the function f(x) = 60x - 3x^2 between x = 6 and x = 19 is -15.
To find the average rate of change for the given function f(x) = 60x - 3x^2 between x = 6 and x = 19, we need to use the formula:
Average Rate of Change = (f(b) - f(a))/(b - a)
where a and b represent the x-values of the interval.
So, let's calculate it step by step:
1. Determine the value of f(a) at x = 6:
f(a) = 60(6) - 3(6)^2
= 360 - 3(36)
= 360 - 108
= 252
2. Determine the value of f(b) at x = 19:
f(b) = 60(19) - 3(19)^2
= 1140 - 3(361)
= 1140 - 1083
= 57
3. Calculate the difference in x-values:
b - a = 19 - 6
= 13
4. Calculate the difference in y-values:
f(b) - f(a) = 57 - 252
= -195
5. Calculate the average rate of change:
Average Rate of Change = (-195) / (13)
= -15
Therefore, the average rate of change for the function f(x) = 60x - 3x^2 between x = 6 and x = 19 is -15.