5 of 5 This Quiz: 5 pts possible This Question: 1 pt Suppose a person wants to t

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5 of 5 This Quiz: 5 pts possible This Question: 1 pt Suppose a person wants to travel D miles at a constant speed of (15 +x) mi/hr, where x could be positive or negative. The time in minutes required to travel D miles is To)-600(15+x)-1. Show that the linear approximation to T at the 15 Recall that the linear approximation L() is equal to T(a)+ T(axx-a). Find T) Substitute a·0 into L(0). Choose the correct answer below. O A. LO)-60D15+0)-60D(15+0)2) O B. Lo)-60D(15+0)(6oD15+).(-o) oc. L(0)=600(15 + 0)-1 + (-60D(15 +0)-2)-(x-0) 0 D. L(0) = 600(15+0)-1-(-600(15 +0,-2)-(X-0) Rewrite L(0) with positive exponents and reduce fractions to lowest terms 40.(Do not factor.) Factor out the common factor from each term of the function Click to select your answerfs). Save for Later MacBook esc Search or enter website n 5

Explanation / Answer

given T(x)= 60D(15+x)-1

=>T'(x)= -60D(15+x)-2

at x=0

T(0)= 60D(15+0)-1

=>T(0)= 4D

T'(x)= -60D(15+x)-2

=>T'(0)= -60D(15+0)-2

=>T'(0)= -4D/15

L(x)=T(0) +(T'(0))(x-0)

=>L(x)=60D(15+0)-1 +( -60D(15+0)-2)(x-0)

=>L(x)=4D +(-4D/15)(x-0)

=>L(x)=4D +(-4Dx/15)

=>L(x)=4D(1 -(x/15))

therefore T(x)L(x)=4D(1 -(x/15))

L(0)=4D +(-4D*0/15)

=>L(0)=4D(1 -(0/15))

=>L(0)=4D

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