How do you find the average rate of change for the function #f(x)=x^2# on the indicated intervals [-2,1]?
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To find the average rate of change of the function ( f(x) = x^2 ) on the interval ([-2, 1]), you 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.
Substitute the values of ( a = -2 ) and ( b = 1 ) into the formula, and then calculate ( f(a) ) and ( f(b) ):
[ f(-2) = (-2)^2 = 4 ] [ f(1) = (1)^2 = 1 ]
Then plug these values into the formula:
[ \text{Average Rate of Change} = \frac{1 - 4}{1 - (-2)} = \frac{-3}{3} = -1 ]
So, the average rate of change of ( f(x) = x^2 ) on the interval ([-2, 1]) is (-1).
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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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