Question

Activity: A Journey Through Calculus from A to Z sin(x-1) :- 1) x< h(x) kr2 - 8x + 6. 13x53 Ver-6 – x2 +5, x>3 Consider f'(x), the derivative of the continuous functionſ defined on the closed interval -6,7] except at x 5. A portion of f' is given in the graph above and consists of a semicircle and two line segments. The function (x) is a piecewise defined function given above where k is a constant The function g(x) and its derivatives are differentiable Selected values for the decreasing function g'(x). the second derivative of g, are given in the table above. (A) Find the value of k such that h(x) is continuous at x = 3. Show your work. (B) Using the value of k found in part (A), is h(x) continuous at x = 17 Justify your answer. C) Is there a time ,-4<<<3 such that "(c) = -27 Give a reason for your answer (D) For each x 2 and x = 4, determine if f(x) has a local minimum, local maximum or neither. Give a reason for your answer.

Answer 1

Date Pago (A) h(x) at x 23 50, continuous h (3) h(35) h(3*) K 19) – 8(3) + 6 = 4 éo - 9+5 9Ra 24 +63 4-9 +5 k=al Bl at xal hlil=hli) (h(t)) A4 I lim Sin (x-1) . x →i -1 hulle h (14), 3(1) - 8+6=0 No it is disconto nuous at xal

. ."(c)-9"(..) &-c. CE (-1,0] - P. 9" (C) 8-10 1-0 g'" (C) 2-2 - in E (-1,0] f(2) is point of maxima f(3) f(3) = f(37) = f(0) I flu) is neither minima nor maxima Iflut) < flul <fli)