Let P(t) represent the price of a share of stock of a corporation at time t. What does each of the following statements tell us about the signs of the first and second derivatives of P(t)? (Hint - you might want to sketch a possible graph.)(a) The price of the stock is rising faster and faster.The sign ofdPdtis ---Select--- vThe sign of(b) The price of theThe sign ofThe sign ofd²pdt²is --Select--- ✓stock is close to bottoming out.dPdtd²pdt²is ---Select--- ✓is ---Select--- ✓

Answered: Image /qna-images/answer/d837f7f0-2dc8-435f-9995-5f1791a0de49.jpg

Answered: Let P(t) represent the price of a share…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Oo.38. Subject:- Advance Mathematic
A snack company is preparing two mixtures of snacks from a supply of 110 pounds pretzels, 30 pounds pistachios, 10 pounds cheese puffs, 60 pounds sesame sticks, and 20 pounds toffee bites. Mixture X contains 55% pretzels, 20% pistachios, 5% cheese puffs, 20% sesame sticks, and no toffee bites, and sells for $7.99 per pound. Mixture Y contains 45% pretzels, 10% pistachios, no cheese puffs, 10 % sesame sticks, and 15% toffee bites, and sells for $5.99 per pound. If x = # of pounds of Snack X and y = # of pounds of Snack Y, determine the constraints on this linear programming problem. Inequality for pretzels [ Choose ] Inequality for pistachios ( Choose] Inequality for cheese puffs ( Choose ) Inequality for sesame sticks [Choose ] Inequality for toffee bits [ Choose ) Non-negativity inequalities [ Choose ] >
2. Consider the three functions below: S(x) = 2r S(z) =r S(z) = 2 (a) Create a t-table for cach of the three functions, using the x-values-2, -1, 0, 1, 2, and 3. (b) Which function appears to be growing the fastest? That is, for which function are the y-values increasing the fastest? (c) On the same set of axes, graph all three of the functions above. Be sure to scale your axes! Was your answer to part b correct?
15. Let a be a real number. We will explore the derivatives of the function f(x) = eax. By using the chain rule, we see (a) What is Recall that the second derivative of a function is the derivative of the deriva- tive function. Similarly, the third derivative is the derivative of the second derivative. (b) What is d² dx² d3 C030 BY NO SA d dx = aeax (eax), the third derivative of eax? (c) Let n be a natural number. Make a conjecture about the nth derivative dn of the function f (x) = eax. That is, what is (eax)? This con- dxn jecture should be written as a self-contained proposition including an appropriate quantifier. (eax), the second derivative of eax? 4.1. The Principle of Mathematical Induction (d) Use mathematical induction to prove your conjecture. 183
Activity 2.5.4. Use known derivative rules, including the chain rule, as needed to answer each of the following questions. a. Find an equation for the tangent line to the curve y = ve* +3 at the point where x = 0. b. If s(t) = 1 represents the position function of a particle moving horizontally along an axis at time t (t2 + 1)3 (where s is measured in inches and t in seconds), find the particle's instantaneous velocity at t = 1. Is the particle moving to the left or right at that instant? c. At sea level, air pressure is 30 inches of mercury. At an altitude of h feet above sea level, the air pressure, P, in inches of mercury, is given by the function P = 30e-0.0000323h. Compute dP/dh and explain what this derivative function tells you about air pressure, including a discussion of the units on dP/dh. In addition, determine how fast the air pressure is changing for a pilot of a small plane passing through an altitude of 1000 feet. d. Suppose that f(x) and g(x) are differentiable…

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