미적분Ⅰ도함수의 활용수능 기출기본 문제 (3점 중반)
삼차함수 극솟값
문제
함수 는 에서 극대이다. 함수 의 극솟값은? (단, 는 상수이다.) [3점] ①②③④⑤
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②
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해설
에서 에서 극대이므로 , , 이때 이므로 에서 또는 함수 의 증가와 감소를 표로 나타내면 다음과 같다.
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| 7fbYQq+Ja2y6KeHMyaMsYHvpSVcipph/A38fFdZpEBZ23r1BxDR7N3AV0bQ1Zttd2iN6PNHV1WUXepaMGa9EQPc+iYBSouh80A== | EFc88wWxQHrsBHEg4FvQKATil0JbBUlx10IQy2LFOq0siqlQweNBvEVqV7tjgO4NJP/rC1pXMJ4qV56bUDl4hg7fGyv9dkHxGw== | CutF/YIYET8uFZQARUPvtGrWUstNF0Dq3a4jzu4usaXza0MQ755sMDdLvO7JRqlqVv2UeCP8Dzn3/Fqp7W71za1V40iT+1yqBQ== | dxPMr5cJ/3YgnWGhh+9v2Wc+BaQBKy12IrWD4Rl5VZ/F08gqUZGBiaiLcMbCZddxyvQGBz7RCPEjhGZ8zesNmhQoeSb38t4pmQ== | tAmJVL6SPLhh5qiHKl1tDkw0za5cDkGCQMuJ/o5vI0nJrrAHeJL22hscfcDswC0lurkYs3Re010rZft+C2aJpVxMC1gYY2cLAw== | 2pnSbVEoWmW27QCbE12EAo8JTBlovd2XWWJscSZDy1+ZSlm6YrHyPmVCD4ccaFooFpj6o+qTeUdeB2NYjWyCnp9Bq76bQYXtsQ== |
| ETv9w7DSqCcsSnzdW7pkRuUhCBNvKvkYjgqhT8+DL0558aj+mtoa7mCyU3GaXq/VxZw8+nsSUllX3PHdug/VNiRBJ6sF3zDfcA== | xCzW+UwiQyFar5L5VxlMPTorE/aiB097wHQXCRVAiWY1OJ0NfN6u02gmb/bxUU8HICFztAVWI3upgc2ImrlRt71Y7TwW+Yd3DA== | 7vli3B80PWTSd/fBZVX2ud0o7fI5uX+AGJ6//jZOmRQ3tef5wzWKrm3I1CBni+x4Z+77rQEGPNWk20uXiJTU8DWGPVwEuzmOew== | nxEWvsgCwbhzbFJNP12fGL0UQ3LB+aEzUB10BdUgahtOPl8NMnyRhQDKv0wqmU/1WzQ48CPQf0TLy+8T7N58RXq1uhQ2DmLWqQ== | 6miC6yym4pIgBOeMENFiuTNZUmkmhuff88WzDbfbIa2tO1wqgs7gjtyByv3X6j9YRvhY2JyHUaGM2iuyZhOXFc66eAfYQfmJVA== | n6RlHL89cxf4FaF2XDn6JuGXRrC/92znk+1PzPLxk0j6b85wdYAY/SQhqTMG6LWMiSeLP7oZlv4K0TwUR9QXAZRbbyxIAmdRPw== |
따라서 함수 는 에서 극솟값 을 갖는다.