Across the Solar System Introduction to Derivatives Directions: Solve the following problem. (3 items it 5 points) Recall that the circumference of a circle is given by f (r) = 2111 where r is the circle's radius. Isz = T1 + AT, . ' 1. Find average rate of change off between T1 and r2. 2. Find instantaneous rate of change off at r = 6,378 (km). 3. Find instantaneous rate of change off at r = 71,492 (km). Rubric for Scorin _: Last two ma'or ste - s of the solution are incorrect Com - lete solution With correct answer n 4 Half of the solution is correct First ma'or ste- of he solution is correct - '- First two ma'or ste . s of the solution are correct \" 35-15:?! v, E7\\'.'r'" ' More Accurate, Please Intermediate and Extreme Values Directions: Fill in the blanks with right expressions. Express answers up to four (4) decimal places. (20 items x 2 points) Perform the bisection method to provide a root for f (x) = x2 + 3x - 2 given & = 0.001. The first three (3) steps were already done in class. Let X1 = 0, X2 = 1, and X3 = 0.5. Then (0.5) = -0.25. . Redefine x1 = 0.5, x3 = 0.75. Then f(0.75) = 0.8125. . Redefine X2 = 0.75, x3 = 0.625. Then f (0.625) = 0.2656. . Redefine X2 = 0.625, X3 = 0.5625. Then f (0.5625) = 0.0039. . Redefine , X3 = Then f (X3) = . Redefine X3 Then f (X3) = Redefine X3- Then f (X3) = . Redefine X3 - Then f (X3) = . Redefine X3 Then f (X3) = . Redefine X3 = Then f (X3) = . Since If (X3)| 2 I. 5 J. 2ex - 2 14. f ( x ) = Slif x # 0 doifx=0atx = 0 N. 2x O. 2ex + 1 5. f(x ) =2e* + 1if x # 0 if x = 0 atx = 0 R. O S. -5 Y. x2 + 2