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Suppose a person wants to travel D miles at a constant speed of (30 + x) mi/hr, where x could be positive or negative. The time in minutes required to travel D miles is T(x) = 60D(30 + x)-1 Show that the linear approximation to Tat the point x=0 is

Suppose a person wants to travel D miles at a constant speed of (30 + x) mi/hr, where x could be positive or negative. The time in minutes required to travel D miles is T(x) = 60D(30 + x)-1 Show that the linear approximation to Tat the point x=0 is

Advanced Engineering Mathematics
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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Suppose a person wants to travel D miles at a constant speed of (30 + x) mi/hr, where x could be positive or negative. The time in minutes required to travel D miles is T(x) = 60D(30 + x)-1. Show that the linear approximation to T at the point x = 0 is T(x) = L(x) = D - 15 Recall that the linear approximation L(x) is equal to T(a) + T'(a)(x - a). Find T'(x). T'(x) = Substitute a =0 into L(x). Choose the correct answer below. O A. L(X) = 60D(30 + 0)¯1 + (- 60D(30 + 0)-2) (60D(30 + 0)1) • (x – 0) O B. L(x) = 60D(30 + 0) + OC. L(x) = 60D(30 + 0)-1- (-60D(30 + 0)2) • (x - 0) - 1 O D. L(x) = 60D(30 + 0) (- 60D(30 + 0)-2) •(x- 0) Rewrite L(x) with positive exponents and reduce fractions to lowest terms. L(x) = (Do not factor.) Factor out the common factor from each term of the function. L(x) =|
Transcribed Image Text:Suppose a person wants to travel D miles at a constant speed of (30 + x) mi/hr, where x could be positive or negative. The time in minutes required to travel D miles is T(x) = 60D(30 + x)-1. Show that the linear approximation to T at the point x = 0 is T(x) = L(x) = D - 15 Recall that the linear approximation L(x) is equal to T(a) + T'(a)(x - a). Find T'(x). T'(x) = Substitute a =0 into L(x). Choose the correct answer below. O A. L(X) = 60D(30 + 0)¯1 + (- 60D(30 + 0)-2) (60D(30 + 0)1) • (x – 0) O B. L(x) = 60D(30 + 0) + OC. L(x) = 60D(30 + 0)-1- (-60D(30 + 0)2) • (x - 0) - 1 O D. L(x) = 60D(30 + 0) (- 60D(30 + 0)-2) •(x- 0) Rewrite L(x) with positive exponents and reduce fractions to lowest terms. L(x) = (Do not factor.) Factor out the common factor from each term of the function. L(x) =|
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