6 Firefox File Edit View History Bookmarks Tools Window Help @ 7.: LI' $113693! Mon 9:46AM E Q 0 EE , O O O Q Wt Homework#2- MAT135, Sectit x + v 6 9 C O [3 https://www.webassign.net/web/Student/AssignmentResponses/last?dep=31602984 5:} a E 18. [-I13 Points] LARPCALC11 2.PS.006. 0/6 Submissions Used One of the fundamental themes of calculus is to find the slope of the tangent line to a curve at a point. To see how this can be done, consider the point (6, 36) on the graph of the quadratic \"5 function for) = x2, as shown in the gure. y (a) Find the slope ml of the line joining (6, 36) and (7, 49). m1 = :1 Is the slope of the tangent line at (6, 36) greater than or less than the slope of the line through (6, 36) and (7, 49)? O greater than 0 less than .' Firefox File Edit View History Bookmarks Tools Window Help @ 7,, LI' \"5? 11% 9:]: Mon 9:46 AM 5 Q 0 EE , O O O U Vh Homework#2- MAT135, Sectit x + v ( 7> C O 6 https://www.webassign.net/web/Student/AssignmentResponses/last?dep=31602984 5:} Q E ents (b) Find the slope m2 of the line joining (6, 36) and (5, 25). m2 = l Is the slope of the tangent line at (6, 36) greater than or less than the slope of the line through (6, 36) and (5, 25)? O greater than ,(s 0 e55 than (c) Find the slope m3 of the line joining (6, 36) and (6.1, 37.21). m3 = Is the slope of the tangent line at (6, 36) greater than or less than the slope of the line through (6, 36) and (6.1, 37.21)? 0 greater than 0 less than (d) Find the slope mh of the line joining (6, 36) and (6 + h, f(6 + h)) in terms of the nonzero number h. (Simplify your answer completely.) mh = (e) Evaluate the slope formula from part (d) for h = 1, 1, and 0.1. h = 1 \"7h = h = 1 mh = h = 0.1 mh = 7 Compare these values with those in parts (a)(c). 0 These values are the same as the values in parts (a)-(c). 0 These values are twice the values in parts (a)(c). 0 These values are half the values in parts (a)(c). 0 These values are the opposite of the values in parts (a)(c). O No comparisons can be made. (f) What can you conclude the slope mtan of the tangent line at (6, 36) to be? Explain. The slope of the tangent line at (6, 36) is mtan = . The slope mh approaches the slope of the tangent line as h approaches :|