124HW13solutions

# 124HW13solutions - Math 124 Homework 13(section 2.5...

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Math 124 Homework 13 (section 2.5), solutions to graded problems 10) Give the signs of the ﬁrst and second derivatives for the following function: Solution: Since f is decreasing , the ﬁrst derivative is negative . As f is concave up , the second derivative is positive 16) 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 abouth the signs of the ﬁrst and second derivatives of P ( t )? (a) “The price of the stock is rising faster and faster” (b) “The price of the stock is close to bottoming out” Solutions: (a) Since the stock is rising, we know that dP dt > 0 .Since it’s rising faster and faster , we know that d 2 P dt 2 > 0 (b) Since the stock is close to bottoming out, we know that P is decreasing and so dP dt < 0 As bottoming out means leveling oﬀ, then P ( t ) has to be approaching a zero slope. Hence P ( t ) must be concave up and d 2 P dt 2 > 0 1

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20) The ﬁgure below gives the position, f ( t ), of a particle at time
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## This note was uploaded on 06/16/2008 for the course MATH 124 taught by Professor Kennedy during the Spring '08 term at Arizona.

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124HW13solutions - Math 124 Homework 13(section 2.5...

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