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Calculus/rate of change
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Question
find the difference quotient and use it to find the average rate of change on the curve between the two values of x.
1.f(x)=4s-5 from x=2 to x=9
so the(f(x+h)-f(x))/h = 4 (from their on I'm stuck#
2. f#x#=3x^2 from x=2 to x=9
so the #f(x+h#-f#x#)/h = 6x+3h #from their on I'm stuck)
1. If the first function is f(x) = 4x-5, and x goes from 2 to 9,
then f(2) = 4*2 - 5 = 8 - 5 = 3, f(9) = 4*9 - 5 = 36 - 5 = 31, and h = 9 - 2 = 7.
Thus, [f(x+h)-f(x)]/h = [f(2+7) - f(2)]/(9-2) = [f(9)-f(2)]/7 = (31-3)/7 = 28/7 = 4.
This means for every increase of 1 in x, the is an increase of 4 in f(x).
This means the rate of change in f(x) is 4.
2. Should this be f(x) = 3x²?
Here, h is again 7 with the first point at x=2 and the second point at x=9.
Now f(9) = 3*9² = 3*81 = 243 and f(2) = 3*2² = 12, so the average rate of change would be
(243-12)/(9-2) = 231/7 = 33.
In this case, the function does not fit the line exactly, but that does give the average rate of change over the intervale.
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