Further Differentiation-summarys, Lecture notes of Mathematics

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PURE 4.4.2. 2 . 4 = is the finetion increasing / decreasing ? Further Differentiation < at a mason /eum au? sche practeal problems inicing roles of change. 4, Tnereasing / decreasing functions yohts) mt dexteasing —— |, ® 9 a Stationary points, Lo cs u r dy de de < gradient of > x cune. ye x dy dx gradient of dy is negative — ¢ ___seeond > gradient of dy is postive de derivative de ay f dy zo ond dy 20 dt f dy zo ond dy 70 de. du de a 2 He —> minimum point 3. Rates of change, aka. a change over time. eg- distance + — Speed time. sped = acceleration. ime The chain rule states « A 6, de dee A | dt dx dt dy ly de ¥ practical applications + vate of increase in size of an oil leak + dhe change in surface area and volume when you blow up a balloon * rate at which water drains from a container