the gradient function Flashcards","topicId":"34cd1221-955f-4eee-9497-155c1b26b13c","topicSlug":"sketch-the-gradient-function","cards":[{"id":"c138cc2f-9959-4905-b18b-5f7ff7ebff1c","cardType":"basic","front":"What does the value of $f'(x)$ represent on $y=f(x)$?","back":"The gradient of the tangent at that value of $x$.","points":1,"mcqOptions":null},{"id":"cd7c5a8d-0f25-4896-8244-922f4056880c","cardType":"basic","front":"If $f'(-1)=4$, which point lies on the gradient graph?","back":"The point $(-1,4)$.","points":1,"mcqOptions":null},{"id":"ed0863d5-8ab0-4ada-bf5d-53c94510afbd","cardType":"basic","front":"Where is the graph of $f'(x)$ when $f(x)$ is increasing?","back":"Above the horizontal axis.","points":1,"mcqOptions":null},{"id":"20f265bb-418e-47ab-ba92-5d0d3c47220d","cardType":"basic","front":"Where is the graph of $f'(x)$ when $f(x)$ is decreasing?","back":"Below the horizontal axis.","points":1,"mcqOptions":null},{"id":"5d4b16ee-c2a2-41f2-b8fe-bb713c73a324","cardType":"cloze","front":"A horizontal tangent to $f(x)$ means $\\text{[...]}$.","back":"A horizontal tangent to $f(x)$ means $\\boxed{f'(x)=0}$.","points":null,"mcqOptions":null},{"id":"2401ff58-3c36-4603-9ea2-d17a65d1ca61","cardType":"basic","front":"How does a stationary point of $f(x)$ appear on its gradient graph?","back":"A horizontal-axis intercept of $f'(x)$.","points":1,"mcqOptions":null},{"id":"f39c652f-7800-432e-98d9-ba1dea6ed995","cardType":"basic","front":"How does $f'(x)$ change sign at a local maximum of $f(x)$?","back":"From positive to negative.","points":1,"mcqOptions":null},{"id":"7a358499-5179-4185-b7cd-02aa00ce0f51","cardType":"basic","front":"How does $f'(x)$ change sign at a local minimum of $f(x)$?","back":"From negative to positive.","points":1,"mcqOptions":null},{"id":"ac87c217-a675-4b74-a5f6-706baa88f3d0","cardType":"cloze","front":"A steep upward slope produces a [ ] value of $f'(x)$.","back":"A steep upward slope produces a large positive value of $f'(x)$.","points":null,"mcqOptions":null},{"id":"c6ba8635-dc1f-4929-8ea0-f0a2ad844cae","cardType":"basic","front":"What happens to $f'(x)$ as a decreasing curve becomes steeper?","back":"It becomes more negative, increasing in magnitude.","points":2,"mcqOptions":null},{"id":"0103eec8-5548-49fa-80bf-f7131e7044c8","cardType":"basic","front":"What happens to $f'(x)$ as an increasing curve becomes nearly horizontal?","back":"It moves towards zero.","points":1,"mcqOptions":null},{"id":"99156b95-d97a-4c80-b9d5-219b58b25319","cardType":"cloze","front":"For $f(x)=mx+c$, the gradient function is $\\text{[...]}$.","back":"For $f(x)=mx+c$, the gradient function is $\\boxed{f'(x)=m}$.","points":null,"mcqOptions":null},{"id":"2eb7c12c-32e2-47d3-b090-0d5bcff9916f","cardType":"basic","front":"What general shape is the derivative of a quadratic?","back":"A linear graph.","points":1,"mcqOptions":null},{"id":"4d2683b8-491f-409e-b4fa-3dcca0400168","cardType":"basic","front":"What general shape is the derivative of a cubic?","back":"A quadratic graph.","points":1,"mcqOptions":null},{"id":"05962c76-85af-43bf-a167-89e90abfa387","cardType":"cloze","front":"Differentiation reduces the degree of a polynomial by [ ].","back":"Differentiation reduces the degree of a polynomial by one.","points":null,"mcqOptions":null},{"id":"d4f659dd-dbfe-4fa6-bd56-e0e12bee7796","cardType":"basic","front":"What is the gradient function of $f(x)=x^2-4x+1$?","back":"$f'(x)=2x-4$.","points":1,"mcqOptions":null},{"id":"92d481c9-e215-400c-a434-d161b156de5d","cardType":"basic","front":"How does $f'(x)$ behave at a stationary point where $f(x)$ changes from increasing to decreasing?","back":"It crosses t

1.9.4 Sketch the gradient function Flashcards

1.9.4 Sketch the gradient function Flashcards