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# 12.07 - Note The exams may not have exactly three questions...

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Note: The exams may not have exactly three questions per day. If there are more questions, they’ll be easier individually! Sometimes finding antiderivatives is tricky: An antiderivative of f ( x ) = (sin x ) ( e x ) is ..?.. (1/2) (sin x ) ( e x ) – (1/2) (cos x ) ( e x ). Questions on section 4.7? Questions on chapter 4? Chapter Review true/false questions on page 248 #1: “If f ( c ) = 0, then f has a local maximum or minimum at c .” ..?.. False; e.g., consider f ( x ) = x 3 at c = 0. If we knew that f ′′ ( c ) was non-zero, we could conclude that f has a local maximum or minimum at c . #2: “If f has an absolute minimum value at c , then f ( c ) = 0.”

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..?.. False; e.g., consider f ( x ) = | x | at c = 0. If we knew that f was differentiable at c , AND we knew that c is not an endpoint, then we could conclude that f ( c ) = 0. #3: “If f is continuous on ( a , b ), then f attains an absolute maximum value f ( c ) and an absolute minimum value f ( d ) at some number c and d in ( a , b ).” ..?.. False; e.g., consider f ( x ) = x on (0,1). The claim becomes true if we replace ( a , b ) by [ a , b ], by the Extreme Value Theorem.
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12.07 - Note The exams may not have exactly three questions...

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