Given #f(x) = 4x + 1# how do you find the average rate of change over [-6,5]?

Answer 1

Memorize this: The average rate of change of function #f# over interval #[a,b]# is #(f(b)-f(a))/(b-a)#.

#(f(5)-f(-6))/(5-(-6)) = 4#
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Answer 2

To find the average rate of change of a function over an interval, you can use the formula:

Average Rate of Change = (f(b) - f(a)) / (b - a)

where f(a) and f(b) are the values of the function at the endpoints of the interval, and a and b are the endpoints themselves.

For the function f(x) = 4x + 1 over the interval [-6, 5], the average rate of change is:

f(-6) = 4(-6) + 1 = -24 + 1 = -23 f(5) = 4(5) + 1 = 20 + 1 = 21

Average Rate of Change = (21 - (-23)) / (5 - (-6)) Average Rate of Change = (21 + 23) / (5 + 6) Average Rate of Change = 44 / 11 Average Rate of Change = 4

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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