:"076cf955-a1e2-4775-a0b3-b86c581fbba3","topicSlug":"differentiation-4","cards":[{"id":"41786acc-f231-42e3-b3a4-5a29d588831e","cardType":"basic","front":"A straight line has gradient 4. What happens to $y$ when $x$ increases by 1?","back":"$$y$ increases by 4.","points":1,"mcqOptions":null},{"id":"534ec124-bdf3-4cdd-ab8b-8623cd7957f1","cardType":"basic","front":"Why does a curve not usually have one gradient describing the whole curve?","back":"Its steepness changes from point to point.","points":2,"mcqOptions":null},{"id":"5e288862-0ec4-4c9b-a70e-eea485620f9b","cardType":"basic","front":"What does $\\frac{dy}{dx}>0$ show about a curve?","back":"The curve is increasing.","points":1,"mcqOptions":null},{"id":"fc94c3fa-fb7d-4b14-98d7-f118d8db18db","cardType":"basic","front":"What does $\\frac{dy}{dx}<0$ show about a curve?","back":"The curve is decreasing.","points":1,"mcqOptions":null},{"id":"615ead44-85f9-4240-a753-372ecbbff21e","cardType":"basic","front":"What does $\\frac{dy}{dx}=0$ show about the tangent and point?","back":"The tangent is horizontal, so the point is stationary.","points":2,"mcqOptions":null},{"id":"ed857f7f-65dc-437b-adc7-8a7129f216d6","cardType":"cloze","front":"A stationary point is [ ].","back":"A stationary point is not necessarily a maximum or minimum.","points":null,"mcqOptions":null},{"id":"981e9698-0fc9-4041-9aeb-81de026b7117","cardType":"basic","front":"What does a large $\\left|\\frac{dy}{dx}\\right|$ show about a curve?","back":"The curve is changing steeply.","points":1,"mcqOptions":null},{"id":"2ce9e0e7-6c23-4990-bf87-0153dad056ef","cardType":"basic","front":"What does a derivative close to zero show about a curve?","back":"The curve is changing slowly.","points":1,"mcqOptions":null},{"id":"84dbd934-c99e-4e40-998f-ef1f8efe74a1","cardType":"cloze","front":"The units of a derivative are $\\text{[...]}$.","back":"The units of a derivative are $\\boxed{\\frac{\\text{units of dependent variable}}{\\text{units of independent variable}}}$.","points":null,"mcqOptions":null},{"id":"85614d2f-2504-4c67-b704-79a51a487428","cardType":"basic","front":"Which line's gradient represents average rate of change over an interval?","back":"The secant joining the interval's endpoints.","points":1,"mcqOptions":null},{"id":"d1ec99de-f517-4559-8b47-cfc5cfad0f7d","cardType":"basic","front":"Which line's gradient represents instantaneous rate of change at a point?","back":"The tangent at that point.","points":1,"mcqOptions":null},{"id":"057d20da-01fe-44b9-88a2-ccc9f3b32fd8","cardType":"cloze","front":"The average rate of change between $x=a$ and $x=b$ is $\\text{[...]}$.","back":"The average rate of change between $x=a$ and $x=b$ is $\\boxed{\\frac{f(b)-f(a)}{b-a}}$.","points":null,"mcqOptions":null},{"id":"56e53015-a998-44af-b1b0-aa22a9ddc28b","cardType":"basic","front":"Given $s(2)=7$ m and $s(5)=31$ m, what is the average velocity from $t=2$ to $t=5$?","back":"$8\\text{ m s}^{-1}$","points":2,"mcqOptions":null},{"id":"09df0053-4ae0-446e-9c9c-b2728b139800","cardType":"cloze","front":"For $P=(a,f(a))$ and $Q=(a+h,f(a+h))$, the secant gradient is $\\text{[...]}$.","back":"For $P=(a,f(a))$ and $Q=(a+h,f(a+h))$, the secant gradient is $\\boxed{\\frac{f(a+h)-f(a)}{h}}$.","points":null,"mcqOptions":null},{"id":"2885ca1e-c5bf-4a0f-88db-ba6ec1a8ac86","cardType":"basic","front":"As $Q$ approaches $P$, what happens to the secant gradient?","back":"It approaches the tangent gradient at $P$.","points":2,"mcqOptions":null},{"id":"eef51e15-b211-4a2a-b8f5-2f35b9ba2887","cardType":"cloze","front":"The derivative at $x=a$ is $\\text{[...]}$.","back":"The derivative at $x=a

1.6.3 Differentiation Flashcards

1.6.3 Differentiation Flashcards