Question

3) (12pts) For the function S(w)=-*+r-15x a) Determine the criticul points for the function. The critical point(s) for the function are at: b) Determine the local cxtrema using the first or second derivative test. Fill in the blanks below with the appropriate critical number. If there is no max or min mark the blank with NA (not applicable). Be sure to show all work when using cither derivative test to carn full credit. Local Maximum(s): Local Minimum(s): 3) Using the same function, Sun=+*+-1 +-157, what are the absolute extremna on the interval (0,6). Show all work to receive full credit

Answer 1

1 (1)-***+-154 '(x) = {{3x) +2x– 15(1) = x2 +2x – 15 3 F"(x) = 2x+2(1) - 0) = 2x +2 (a)To find the critical points, f '(x) = 0 x2+2x–15=0 (x+5)(x-3) = 0 x=-5,3 The critical points for the function are at x = -5,3 (b) To find the local maxima and minima. | "(-5) = 2(-5)+2 =-10+2 = -8 <0 f "(3) = 2(3)+2 = 6+2 = 8 > 0 175 3 (-5) = f(-3)*+1-51*-13(-5) = 1 $(3) = $(3)*+(3) 2–15(3) = -27 175 Local maximum is at x = -5.Local minimum is -27 at x = 3. 3 (c) To find the absolute extrema on the interval (0,6] 175 3 f(0) = $(0) +0°-15(0) = 0 f(-5) = f(-5)+(-5) 2– 15(-5) = $(3)= }(3)+(3) 2 - 15(3) = -27 $(6) =$(6)° +(6) *–15(6) = 18 The absolute maximum is 175 and the absolute minimum is -27 3