How do you find the average rate of change of #f(x)=2x^2+2# from -3 to 0?

Answer 1

#-6#

Average rate of change is given by the formula: #(f(b)-f(a))/(b-a)#
In our case, #b=-3# and #a=0#. First, we find #f(b)# and #f(a)#: #f(b)=f(-3)=2(-3)^2+2=20# #f(a)=f(0)=2(0)^2+2=2#
Plugging all the info into the formula: #(20-2)/(-3-0)=18/-3=-6#. The negative sign means the function is decreasing over the interval.
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Answer 2

To find the average rate of change of (f(x) = 2x^2 + 2) from -3 to 0, we first find the values of the function at the given points:

(f(-3) = 2(-3)^2 + 2 = 2(9) + 2 = 18 + 2 = 20)

(f(0) = 2(0)^2 + 2 = 2(0) + 2 = 0 + 2 = 2)

Then, we calculate the change in the function value over the given interval:

Change in (f(x) = f(0) - f(-3) = 2 - 20 = -18)

Next, we calculate the change in the input value over the interval:

Change in (x = 0 - (-3) = 3)

Finally, we find the average rate of change by dividing the change in the function value by the change in the input value:

Average Rate of Change (= \frac{Change , in , f(x)}{Change , in , x} = \frac{-18}{3} = -6)

Therefore, the average rate of change of (f(x) = 2x^2 + 2) from -3 to 0 is -6.

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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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