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How do you find the average rate of change of #f(x)= x^3 -2x# over the interval [0,4]?

Answer 1

#14#

#"The average rate of change in the closed interval "[a,b]# #"is a measure of the slope of the secant line joining the"# #"points "(a,f(a))" and "(b,f(b))#

#"average rate of change "=(f(b)-f(a))/(b-a)#

#"here "[a,b]=[0,4]#

#f(b)=f(4)=4^3-8=56#

#f(a)=f(0)=0#

#"average rate of change "=(56-0)/4=14#

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Answer 2

Cameron Alexander

To find the average rate of change of the function (f(x) = x^3 - 2x) over the interval ([0, 4]), you can use the formula:

[\text{Average rate of change} = \frac{f(b) - f(a)}{b - a}]

Where (a) and (b) are the endpoints of the interval. In this case, (a = 0) and (b = 4).

First, find (f(0)) and (f(4)):

[f(0) = (0)^3 - 2(0) = 0] [f(4) = (4)^3 - 2(4) = 64 - 8 = 56]

Now, substitute these values into the formula:

[\text{Average rate of change} = \frac{f(4) - f(0)}{4 - 0} = \frac{56 - 0}{4} = \frac{56}{4} = 14]

So, the average rate of change of (f(x) = x^3 - 2x) over the interval ([0, 4]) is (14).

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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.