Applications differential calculus ppt8/19/2023 ![]() ![]() It has millions of presentations already uploaded and available with 1,000s more being uploaded by its users every day. is a leading presentation sharing website. Hence the cut out squares should be 2cm in Resulting box has the largest possible volume. Out from each corner and the sides folded up.įind the size of the cut out squares so that the An open box with a rectangular base is to beĬonstructed from a rectangular piece of card Determine the local extrema and if necessary theġ.Find the critical numbers for the function.Identify the variables to be optimised and thenĮxpress this variable as a function of one of the.Try to translate any information in the question.Help you introduce any variables you are likely Often in the context in which they are set can be Optimisation problems appear in many guises Provides an efficient technique to finding the If the second derivative test is easier toĭetermine than making a table of signs then this Of the nature of the stationary point that must Suitable interval centred at a provides evidence If extrema occurs at end points then they are end Points of the function, turning points orĬritical points within the interval of the Local extreme values occur either at the end Left derivativeĮ is not a critical point as it is not in the TJĪ critical point of a function is any point (a,į(a)) where f (a) 0 or where f (a) does notĬ (1,1) f (1) does not exist. Hence the velocity is decreasing when t lt 2Īt t 0, the particle is 1m from the origin withĪ velocity of 9ms-1 decelerating at a rate ofĪt t 1, the particle is 5m from the origin atĪt t 2, the particle is 3m from the origin withĪ velocity of -3ms-1 with zero acceleration.Īt t 3, the particle is 1m from the origin atĪt t 4, the particle is 5m from the origin withĪ velocity of 9ms-1 accelerating at a rate of Hence the distance S is increasing when t lt 1 and The acceleration is zero when t 2 seconds. The velocity is zero when t 1 or 3 seconds. ![]() Describe the motion of the particle during the.When is the velocity of the body decreasing?.Find when (i) the velocity and (ii) the.where S represents its displacement in metres.A body travels along a straight line such that.Hence the particle is 5m from the origin at the Calculate the velocity and acceleration of the.How far from the origin is the particle at the.where x represents its displacement in metresįrom the origin t seconds after observation.A particle travels along the x axis such that.Note The use of units MUST be consistent. Velocity is a rate of change of displacement.Īcceleration is a rate of change of velocity. Let displacement from an origin be a function of When a approaches e, the limit approaches 1.ĭifferentiating both sides with respect to x. The functions are otherwise continuous but for Of sec and cosec functions have breaks in them. Unlike the sine and cosine functions, the graphs exercise 5A Questions 1 to 4 and 7 Pageģ8 Exercise 5B Questions 1 to 3 TJ Exercise 5 exercise 4A Questions 1, 2(b) and 3 Pageģ6 exercise 4B Questions 1(b), 3 and 4 TJ Negative and the right derivative is positive.įor a function to be differentiable, it must beĭifferentiation reminder Exercise 3A Here, tan(x) has breaks in the graph where theĪlthough the graph is continuous, the derivativeĪt zero is undefined as the left derivative is The derivative, or derived function of f(x)įurther practice on page 29 Exercise 1A Questionsġ, 4, 5 and 7 TJ Exercise 1 But not just Yet.
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