Increasing and decreasing functions Flashcards","topicId":"1891ace0-7f48-449c-bf46-9d6293dac161","topicSlug":"increasing-and-decreasing-functions","cards":[{"id":"ac6efeaf-1477-49f9-8865-332b294a2ca1","cardType":"basic","front":"What does $f'(x)>0$ imply about $f(x)$?","back":"The function is increasing.","points":1,"mcqOptions":null},{"id":"206b7ba2-5412-4a0d-b471-8ff3e8b44cae","cardType":"basic","front":"What does $f'(x)<0$ imply about $f(x)$?","back":"The function is decreasing.","points":1,"mcqOptions":null},{"id":"63de5e85-1931-458a-bc97-61cd9db94b49","cardType":"cloze","front":"If $f'(x)=0$, the curve has a [ ].","back":"If $f'(x)=0$, the curve has a horizontal tangent.","points":null,"mcqOptions":null},{"id":"73cae876-793c-4eee-bb6f-33415a613d7c","cardType":"basic","front":"In which direction is increasing or decreasing judged?","back":"As $x$ moves from left to right.","points":1,"mcqOptions":null},{"id":"14bc0169-4b5a-45b1-bfc3-8334b72fb74a","cardType":"cloze","front":"For $y=f(x)$, $\\text{[...]}$ gives the curve's gradient at each $x$.","back":"For $y=f(x)$, $\\boxed{f'(x)}$ gives the curve's gradient at each $x$.","points":null,"mcqOptions":null},{"id":"5a851c45-5f08-404f-b9b2-3f48ffa0571e","cardType":"basic","front":"Besides $f'(x)=0$, what can make an input a critical value?","back":"The derivative does not exist there.","points":1,"mcqOptions":null},{"id":"a7e08ae8-0092-4c7b-8e7c-8bbfcb449c61","cardType":"cloze","front":"Solutions of $f'(x)=0$ give the [ ] between possible behaviours, not the behaviours themselves.","back":"Solutions of $f'(x)=0$ give the boundaries between possible behaviours, not the behaviours themselves.","points":null,"mcqOptions":null},{"id":"54d6423f-56cf-4a9b-a0db-696624e9da25","cardType":"basic","front":"How is a test value used to classify an interval?","back":"Substitute it into $f'(x)$ and determine the sign.","points":2,"mcqOptions":null},{"id":"f95a58e7-0cbd-4f99-bff7-25349423a50a","cardType":"cloze","front":"One test value per interval is sufficient if $f'(x)$ is continuous and has [ ] in that interval.","back":"One test value per interval is sufficient if $f'(x)$ is continuous and has no other zeros in that interval.","points":null,"mcqOptions":null},{"id":"5b0eb539-4aa1-409b-a31a-ae508a75b91d","cardType":"basic","front":"What is the first step when finding increasing and decreasing intervals?","back":"Differentiate to find $f'(x)$.","points":1,"mcqOptions":null},{"id":"83daa499-c6fd-4f3f-80a9-7e0ae1783ba2","cardType":"cloze","front":"Critical values are used to [ ] for sign testing.","back":"Critical values are used to divide the domain into intervals for sign testing.","points":null,"mcqOptions":null},{"id":"9962cf5e-0a0b-491d-a21d-5f9f31f56e60","cardType":"basic","front":"How does a restricted domain affect the reported intervals?","back":"Report only intervals inside the given domain.","points":2,"mcqOptions":null},{"id":"bd3154ff-fe1d-4025-babd-90be5074ecf8","cardType":"basic","front":"Why are isolated zeros of $f'(x)$ usually excluded from intervals where $f'(x)>0$?","back":"Because $f'(x)>0$ is a strict inequality.","points":2,"mcqOptions":null},{"id":"936ab9eb-db20-4948-80bf-bacd0459c5f9","cardType":"basic","front":"What does $f(x)=x^3$ show about an isolated zero of $f'(x)$?","back":"It need not stop the function increasing

1.7.15 Increasing and decreasing functions Flashcards

1.7.15 Increasing and decreasing functions Flashcards