:"1db49534-5cd1-48cb-b44d-bef488f1935a","topicSlug":"differentiation-8","cards":[{"id":"5b18ab49-da08-46b4-9a93-3813c47e23aa","cardType":"cloze","front":"Where $f'(x)>0$, the function is [ ].","back":"Where $f'(x)>0$, the function is increasing.","points":null,"mcqOptions":null},{"id":"35ad64f1-054e-40fd-8e8c-d630695f797a","cardType":"cloze","front":"Where $f'(x)<0$, the function is [ ].","back":"Where $f'(x)<0$, the function is decreasing.","points":null,"mcqOptions":null},{"id":"6019640c-00ce-412e-9ac3-4114cfc46a11","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":"d91ddae1-0496-4fd8-851a-1d9878cc5aaa","cardType":"basic","front":"For $f(x)=x^3-6x$, find $f'(x)$.","back":"$f'(x)=3x^2-6$","points":1,"mcqOptions":null},{"id":"596b500f-e2cc-4105-a770-bb0993a9a6ec","cardType":"basic","front":"For $f(x)=x^3-6x$, is the curve rising or falling at $x=2$?","back":"Rising, since $f'(2)=6>0$.","points":2,"mcqOptions":null},{"id":"5223a41c-d3de-4849-aa4a-152826ef3cbd","cardType":"basic","front":"On which interval is $f(x)=x^2$ increasing?","back":"$x>0$","points":1,"mcqOptions":null},{"id":"d49005b1-4674-4e72-8114-7fef76707246","cardType":"basic","front":"On which interval is $f(x)=x^2$ decreasing?","back":"$x<0$","points":1,"mcqOptions":null},{"id":"1378a5e6-9ca9-46ed-a63b-c8435f234872","cardType":"basic","front":"Which values should divide the domain before testing the sign of $f'(x)$?","back":"

Values where $f'(x)=0$
Values where $f'(x)$ is undefined

","points":3,"mcqOptions":null},{"id":"b2800578-8965-4e9e-80ee-bd49e67cbf46","cardType":"basic","front":"Why is one test value sufficient within each interval of a derivative sign diagram?","back":"The sign of $f'(x)$ remains unchanged between consecutive critical values.","points":2,"mcqOptions":null},{"id":"e1702090-d315-4226-90d1-29c4921a0b2a","cardType":"cloze","front":"A change in $f'(x)$ from positive to negative identifies a [ ].","back":"A change in $f'(x)$ from positive to negative identifies a local maximum.","points":null,"mcqOptions":null},{"id":"17d5befb-2fa6-4fd9-b485-ed4f075d03f7","cardType":"cloze","front":"A change in $f'(x)$ from negative to positive identifies a [ ].","back":"A change in $f'(x)$ from negative to positive identifies a local minimum.","points":null,"mcqOptions":null},{"id":"9a0bfbc2-a6d1-4141-a551-5dac7433076d","cardType":"basic","front":"For $f(x)=x^3-3x^2-9x+4$, find the stationary values of $x$.","back":"$x=-1$ and $x=3$","points":2,"mcqOptions":null},{"id":"2bafddfc-d9aa-4037-baf1-6dd7ecefa676","cardType":"basic","front":"Where is $f(x)=x^3-3x^2-9x+4$ increasing?","back":"$x<-1$ or $x>3$","points":2,"mcqOptions":null},{"id":"2d48a678-55b9-4b22-9066-a8585db8288a","cardType":"basic","front":"Where is $f(x)=x^3-3x^2-9x+4$ decreasing?","back":"$-1","points":1,"mcqOptions":null},{"id":"e4e04a83-b49e-4ebc-97db-99c62d643033","cardType":"basic","front":"For $f(x)=2x^3+3x^2-12x$, factorise $f'(x)$.","back":"$f'(x)=6(x+2)(x-1)$","points":2,"mcqOptions":null},{"id":"874496d6-89a7-4637-a408-5defd7b78a15","cardType":"basic","fro

1.6.7 Differentiation Flashcards

1.6.7 Differentiation Flashcards