dient of a curve at a point Flashcards","topicId":"b5dc77d4-8c27-4b3d-9f7d-125e7f289d0c","topicSlug":"gradient-of-a-curve-at-a-point","cards":[{"id":"73de7061-58d4-4763-985f-74d42a150b19","cardType":"cloze","front":"For two points $(x_1,y_1)$ and $(x_2,y_2)$, the straight-line gradient is $\\text{[...]}$.","back":"For two points $(x_1,y_1)$ and $(x_2,y_2)$, the straight-line gradient is $\\boxed{\\frac{y_2-y_1}{x_2-x_1}}$.","points":null,"mcqOptions":null},{"id":"a6295664-87b9-4e94-9f8e-57cd6ee9ad37","cardType":"basic","front":"Find the gradient of the line through $(2,5)$ and $(8,17)$.","back":"The gradient is $2$.","points":2,"mcqOptions":null},{"id":"b5f07fd0-8bce-4054-bb51-c9276481305a","cardType":"cloze","front":"Any two distinct points on a straight line give the same gradient because its steepness is [ ].","back":"Any two distinct points on a straight line give the same gradient because its steepness is constant.","points":null,"mcqOptions":null},{"id":"56d9ce79-ed52-43d3-b34f-21be5d16a4a0","cardType":"cloze","front":"For a curve, the required [ ] must be specified because its gradient can change.","back":"For a curve, the required point must be specified because its gradient can change.","points":null,"mcqOptions":null},{"id":"c67d771d-cad5-4ff1-9a90-8cf5e01427d2","cardType":"basic","front":"Why does a tangent give the gradient of a curve at a point?","back":"It has the same instantaneous direction as the curve.","points":2,"mcqOptions":null},{"id":"5beb503e-a296-4d1d-88bf-b403a0fcf035","cardType":"basic","front":"Can a tangent cross the curve at the point of contact?","back":"Yes - a tangent can cross the curve.","points":1,"mcqOptions":null},{"id":"29cbe635-2947-43eb-a775-a0ffc63a3138","cardType":"basic","front":"Which points should be used to calculate a drawn tangent's gradient?","back":"Points on the tangent - they need not lie on the curve.","points":1,"mcqOptions":null},{"id":"031b7c62-8a5c-4458-8874-e6f22bd5c562","cardType":"cloze","front":"Joining two points on a curve gives the gradient of a [ ], not the exact gradient at either point.","back":"Joining two points on a curve gives the gradient of a chord, not the exact gradient at either point.","points":null,"mcqOptions":null},{"id":"c64236fc-6afc-46e1-bcc7-f09942c0d8a5","cardType":"basic","front":"What does a positive tangent gradient show?","back":"The curve is increasing locally.","points":1,"mcqOptions":null},{"id":"ef0a8519-1722-433a-b0f9-32598ed4735f","cardType":"basic","front":"What does a negative tangent gradient show?","back":"The curve is decreasing locally.","points":1,"mcqOptions":null},{"id":"8548a66c-a8c6-4c8a-a1d9-bceefd24a58d","cardType":"basic","front":"What does a zero tangent gradient show?","back":"The tangent is horizontal, so the point is stationary.","points":2,"mcqOptions":null},{"id":"949eafb4-4f29-449f-95c5-9efa2d3d1ba3","cardType":"basic","front":"What cannot be determined from a zero gradient alone?","back":"Whether it is a maximum, minimum or another stationary point.","points":1,"mcqOptions":null},{"id":"a6c8b90e-ec82-48ff-961c-3112869fe023","cardType":"basic","front":"Does a point's $y$-coordinate determine the sign of its gradient?","back":"No - height gives position; gradient gives direction and steepness.","points":2,"mcqOptions":null},{"id":"a7d25ffe-f0d7-4070-9f6b-38b038cf5ae3","cardType":"basic","front":"Why use well-separated points on a drawn tangent?","back":"It reduces the effect of drawing and co

1.9.1 Gradient of a curve at a point Flashcards

1.9.1 Gradient of a curve at a point Flashcards