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(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.

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(Your brain is too mainstream and it probably hurts)

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  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

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