cId":"673495b4-1889-436b-a43b-a0f7dcecb2a2","topicSlug":"stationary-points","cards":[{"id":"dfc722fc-4b20-4304-a399-949ff2b1cb58","cardType":"cloze","front":"At a stationary point, $\\text{[...]}$.","back":"At a stationary point, $\\boxed{\\frac{dy}{dx}=0}$.","points":null,"mcqOptions":null},{"id":"b530a9c7-89e3-4922-b391-7ed5f843e40c","cardType":"basic","front":"What does a zero gradient tell you about the tangent to a curve?","back":"The tangent is horizontal.","points":1,"mcqOptions":null},{"id":"b7c7dab8-ce3d-488b-be09-9131762724fa","cardType":"basic","front":"What does a positive value of $\\frac{dy}{dx}$ show?","back":"The curve is increasing.","points":1,"mcqOptions":null},{"id":"3d5b2eff-cdfe-4edc-991d-baf2238af0b8","cardType":"basic","front":"What does a negative value of $\\frac{dy}{dx}$ show?","back":"The curve is decreasing.","points":1,"mcqOptions":null},{"id":"e13dd7c7-e2ae-4210-afeb-6e9a083836f9","cardType":"cloze","front":"A point that is highest only within its nearby part of a curve is a [ ].","back":"A point that is highest only within its nearby part of a curve is a local maximum.","points":null,"mcqOptions":null},{"id":"743cfc8b-989d-4b5f-8be2-7ae3f5997140","cardType":"basic","front":"After solving $\\frac{dy}{dx}=0$, how is the corresponding $y$-coordinate found?","back":"Substitute the value of $x$ into the original equation $y=f(x)$.","points":1,"mcqOptions":null},{"id":"14bdb27d-75b3-4f5c-a330-0a69ee0ffe5e","cardType":"basic","front":"Why should a stationary value of $x$ not be substituted into $\\frac{dy}{dx}$ to find its $y$-coordinate?","back":"The derivative gives the gradient, not the curve's height.","points":2,"mcqOptions":null},{"id":"daf3c816-d524-4672-befe-cd74bcdbd4a5","cardType":"cloze","front":"At a local maximum, the sign of $\\frac{dy}{dx}$ changes from [ ].","back":"At a local maximum, the sign of $\\frac{dy}{dx}$ changes from positive to negative.","points":null,"mcqOptions":null},{"id":"d8042b9f-87ad-4747-981f-00bbd6945605","cardType":"cloze","front":"At a local minimum, the sign of $\\frac{dy}{dx}$ changes from [ ].","back":"At a local minimum, the sign of $\\frac{dy}{dx}$ changes from negative to positive.","points":null,"mcqOptions":null},{"id":"8a4a5357-54c6-4d3f-891b-0b52d645e350","cardType":"basic","front":"How can $\\frac{dy}{dx}$ be used to classify a stationary point?","back":"Check its sign on either side of the stationary value.","points":2,"mcqOptions":null},{"id":"c44bea7f-cdee-4b24-b546-a7d035873aae","cardType":"basic","front":"What does the second derivative measure?","back":"How the gradient is changing.","points":1,"mcqOptions":null},{"id":"d9e72db0-8472-4b16-bb29-7ecd645a182a","cardType":"basic","front":"At a stationary point, what does $\\frac{d^2y}{dx^2}<0$ imply?","back":"The point is a local maximum.","points":1,"mcqOptions":null},{"id":"c3790352-b187-426b-a147-6eae3e3b32be","cardType":"basic","front":"At a stationary point, what does $\\frac{d^2y}{dx^2}>0$ imply?","back":"The point is a local minimum.","points":1,"mcqOptions":null},{"id":"6e145c48-0630-4086-8ffc-a5fccfb04dc3","cardType":"cloze","front":"If $\\frac{d^2y}{dx^2}=0$ at a stationary point, the second derivative test is [ ].","back":"If $\\frac{d^2y}{dx^2}=0$ at a stationary point, the second derivative test is inconclusive.","points":null,"mcqOpt

1.7.14 Stationary points Flashcards

1.7.14 Stationary points Flashcards