미적분Ⅰ도함수의 활용수능 기출기본 문제 (3점 중반)

삼차함수 극솟값

문제

함수 f(x)=x3+ax+9f \left( x \right) = x ^{3} + ax + 9x=1x = - 1에서 극대이다. 함수 f(x)f \left( x \right)의 극솟값은? (단, aa는 상수이다.) [3점] 667788991010

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아직 올라온 파일이 없습니다.

해설

f(x)=x3+ax+9f \left( x \right) = x ^{3} + ax + 9에서 f(x)=3x2+af' \left( x \right) = 3 x ^{2} + a x=1x = - 1에서 극대이므로 f(1)=0f' \left( - 1 \right) = 0, 3+a=03 + a = 0, a=3a = - 3 이때 f(x)=3x23=3(x+1)(x1)f' \left( x \right) = 3 x ^{2} - 3 = 3 \left( x + 1 \right) \left( x - 1 \right)이므로 f(x)=0f' \left( x \right) = 0에서 x=1x = - 1 또는 x=1x = 1 함수 f(x)f \left( x \right)의 증가와 감소를 표로 나타내면 다음과 같다.

V22793XxDkSru1h3w+RsSK8VciRTUje/Kyi+3sq7RhkVUKUHMhtcLUp9yS2SSFTa5kFTgaiOPIUam0Ym39p2Rq2ErvR2TjWMig==Ie5QOHbBIcgJwlwJUjnyJ+0zvwrX1v7uR9HmEEeFrGbaR0wcMqagHhNw7uCgcpaA8GexhF5NVkLQdd4FZcYmJswsm931T6shaw==Y82XHIJm2liwTSDX6lqAlqNq06QIZ2FMssLi2C9RpgpAjywkEaZQLaRLmdHY2uv0/ektMufOnqme4UH03XLCK3M1u1KpFkCqFg==TmUlv8SnMDgmgHzuOjUTP36FI+DCJlAYCDeKiqS2jwg9t3AvJsndmGceL7Bqy3ACL5Vv9IiYqXCLnOKunV1Hh/4oBiqxuqtHwA==qyacnsy87kiiAgtVrZcpDbUU6KXoraZs0XmLJby5GH/YtfAa0EAP21T5uYY1lFCUIEGmgP77NibFprkJoyTwMoZhH6cc69lg/w==XiFCRMUM6bEJPn5CNQsBd8ugbc25mJeCoE/BZ+/Kfk+ep7DfamHnHhzwnQpuwYGTONd0iL3lqmwmC/VVl14ejbyAJm8U+rNRjQ==
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 f(x)f \left( x \right)x=1x = 1에서 극솟값 77을 갖는다.

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