1 / 8

(Your brain is too mainstream and it probably hurts)

(Your brain is too mainstream and it probably hurts). About This Problem. This FRQ focuses on chapter four: Antiderivatives. Some of the topics mentioned include average value, left Riemann sum, the Mean Value Theorem and the First Fundamental Theorem of Calculus. Part A.

sebastian-spears
Download Presentation

(Your brain is too mainstream and it probably hurts)

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. (Your brain is too mainstream and it probably hurts)

  2. About This Problem This FRQ focuses on chapter four: Antiderivatives. Some of the topics mentioned include average value, left Riemann sum, the Mean Value Theorem and the First Fundamental Theorem of Calculus.

  3. Part A • Estimate W’(12) and interpret its meaning. Here we use the formula f ’(c) = f(b) – f(a) because we can apply the Mean Value Theorem. b – a MVT states that if f(x) is defined and continuous on the interval [a, b] and differentiable on (a,b), then there is at least one number c in which f ’(c) = f(b) – f(a) b – a W’(12) fits within the (9,15) interval and therefore a = 9, b =15, f(a) = 61.8 and f(b) = 67.9 The water’s temperature is increasing at a rate of 1.017 degrees Fahrenheit when t=12 minutes.

  4. Part B b) Evaluate and interpret its meaning. According to the first FTC which states W(20) – W(0) can be used to evaluate the integral. W(20) – W(0) 71.0 –55.0 = 16 degrees Fahrenheit The water’s temperature increased by 16 degrees during the interval t=0 and t=20 minutes.

  5. Part C C) Evaluate using a left Riemann sum with four subintervals. Is it an under or overestimate? Explain. Our four intervals are (0,4) (4,9)(9,15) and (15,2o) Left Riemann Sum formula: (x2 – x1) f(x1) It’s an underestimate because the function W is strictly increasing and the value of the average is smaller than 71.

  6. Part D d) Given on 20 < t < 25, what’s the temperature when t =25? We first plug W ‘(t) into y = and then press graph. Next we press 2nd, trace and 7. We plug in our limits and press enter. This answer is incomplete, however, since W’(t) = 71 between the 0< t <20 interval. So we use 71 as our initial condition and add it to Therefore 71 + 2.0431547 = 73.0431547 W(25) = 73.043

  7. Bibliography • http://apcentral.collegeboard.com/apc/public/repository/ap12_calculus_ab_scoring_guidelines.pdf • http://www.presentationfx.com/math.html

More Related