If f(x) is continuous on the interval [4, 7], how many of the following statements are true?
A. f(x) has a maximum value on [4, 7]. B. f(x) has a minimum value on [4, 7].
C. f(7) > f(4) D. lim f(x) = f(6)
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To determine the number of true statements, we need to analyze each statement separately.
A. To determine if f(x) has a maximum value on the interval [4, 7], we can use the Extreme Value Theorem. According to the theorem, if f(x) is continuous on a closed interval [a, b], then it has a maximum and minimum value on that interval. Since f(x) is continuous on [4, 7], statement A is true.
B. Similar to statement A, by the Extreme Value Theorem, if f(x) is continuous on a closed interval [a, b], it has a maximum and minimum value on that interval. Therefore, statement B is also true.
C. To determine if f(7) > f(4), we can directly compare the function values at those points. Since we don't have any specific information about the function f(x), we cannot definitively say whether f(7) is greater than f(4). Therefore, we cannot conclude the truth of statement C.
D. To evaluate the limit lim f(x) = f(6), we need to determine the behavior of the function as x approaches 6. This requires additional information about the function f(x) or its definition. Without any further information, we cannot determine the truth of statement D.
In conclusion, statements A and B are definitely true, while statements C and D cannot be determined with the given information.
Well
y = 3 is continuous
graph it from x = 4 to x = 7
A does it have a maximum?
B does it have a minimum?
C is it bigger at 7 than at 4?
D is 3 equal to 18?