https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:functions/x2f8bb11595b61c86:intervals-where-a-function-is-positive-negative-increasing-or-decreasing/v/increasing-decreasing-positive-and-negative-intervals 2021-05-05T14:53:16Z Increasing, decreasing, positive or negative intervals Function values can be positive or negative, and they can increase or decrease as the input increases. Here we introduce these basic properties of functions. video https://cdn.kastatic.org/googleusercontent/KeH1ZaAKr8tifSfCyQBg3KbdJ8WLhEvNRU-cWfp56Vjz8PpbDAWlHyhmMafXzMNAJSiLalC1tJpIeMk_lGjb9n_X Increasing, decreasing, positive or negative intervals Function values can be positive or negative, and they can increase or decrease as the input increases. Here we introduce these basic properties of functions. https://cdn.kastatic.org/ka-youtube-converted/KxOp3s9ottg.mp4/KxOp3s9ottg.mp4 356 Increasing and decreasing functions https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:functions/x2f8bb11595b61c86:intervals-where-a-function-is-positive-negative-increasing-or-decreasing/e/increasing-decreasing-intervals-of-functions 2025-08-29T01:00:50.274419509Z Increasing and decreasing intervals Highlight intervals on the domain of a function where it's only increasing or only decreasing. Sid Patel exercise https://www.khanacademy.org/math/ap-calculus-ab/ab-diff-analytical-applications-new/ab-5-3/v/finding-increasing-interval-given-derivative 2022-10-07T01:21:57.107451925Z Finding increasing interval given the derivative Sal is given that the derivative of function g, is g'(x)=x²/(x-2)³. He uses that to find the intervals where g is increasing, by looking for the intervals where g' is positive. video https://cdn.kastatic.org/ka_thumbnails_cache/0d4960bf-6961-4eb4-b384-114325f79f5b_1280_720_base.png Finding increasing interval given the derivative Sal is given that the derivative of function g, is g'(x)=x²/(x-2)³. He uses that to find the intervals where g is increasing, by looking for the intervals where g' is positive. https://cdn.kastatic.org/ka-youtube-converted/sOluh1zX5tE.mp4/sOluh1zX5tE.mp4 360 Increasing and decreasing functions https://www.khanacademy.org/math/ap-calculus-ab/ab-diff-analytical-applications-new/ab-5-3/v/increasing-decreasing-intervals-given-the-function 2022-10-07T01:21:57.107451925Z Finding decreasing interval given the function Sal finds the intervals where the function f(x)=x⁶-3x⁵ is decreasing by analyzing the intervals where f' is positive or negative. video https://cdn.kastatic.org/ka_thumbnails_cache/956d78cb-de91-4998-8035-0b2c6035ca48_1280_720_base.png Finding decreasing interval given the function Sal finds the intervals where the function f(x)=x⁶-3x⁵ is decreasing by analyzing the intervals where f' is positive or negative. https://cdn.kastatic.org/ka-youtube-converted/Fk4pn8ZOy1w.mp4/Fk4pn8ZOy1w.mp4 318 Increasing and decreasing functions https://www.khanacademy.org/math/ap-calculus-ab/ab-diff-analytical-applications-new/ab-5-9/v/calculus-based-justification-for-function-increasing 2022-10-07T01:21:57.107451925Z Calculus-based justification for function increasing A calculus-based justification is when we explain a property of a function f based on its derivative f'. See a good example (and a few wrong ones) for how to do this when explaining why a function increases. video https://cdn.kastatic.org/ka_thumbnails_cache/b744653e-ba42-447c-8f9f-db89813a9fe3_1280_720_base.png Calculus-based justification for function increasing A calculus-based justification is when we explain a property of a function f based on its derivative f'. See a good example (and a few wrong ones) for how to do this when explaining why a function increases. https://cdn.kastatic.org/ka-youtube-converted/qLhZdSNDQ0M.mp4/qLhZdSNDQ0M.mp4 192 Increasing and decreasing functions https://www.khanacademy.org/math/ka-math-class-12/x6f66cbee9a2f805b:application-of-derivatives-ncert-new/x6f66cbee9a2f805b:increasing-and-decreasing-functions/v/interpreting-slope-of-a-curve-exercise 2021-06-21T15:30:28Z Derivative & the direction of a function Sal analyzes various graphs to find intervals where the derivative of the graphed function is positive or negative. Sal Khan video https://cdn.kastatic.org/googleusercontent/rVy9kIumDqsru0eJtZaYeF0sco_O-k0UUFbSAFMSYdKfJJq1usPmK0edySu3KJWnmIl1p5icJexsFP2wjAZaC67P8Q Derivative & the direction of a function Sal analyzes various graphs to find intervals where the derivative of the graphed function is positive or negative. https://cdn.kastatic.org/ka-youtube-converted/CpDfay5NeCg.mp4/CpDfay5NeCg.mp4 171 Increasing and decreasing functions https://www.khanacademy.org/math/ap-calculus-ab/ab-diff-analytical-applications-new/ab-5-3/a/increasing-and-decreasing-intervals-review 2021-04-29T07:53:17Z Increasing & decreasing intervals review Review how we use differential calculus to find the intervals where a function increases or decreases. article https://www.khanacademy.org/math/ap-calculus-ab/ab-diff-analytical-applications-new/ab-5-3/e/find-increasing-and-decreasing-intervals 2025-05-05T08:14:25.350149109Z Increasing & decreasing intervals Find the intervals in which a function (given algebraically) is increasing or decreasing. Tomer Gal exercise