Question

Consider the function y 5 + 6x - 8x3 Find the largest open intervals on which the function is increasing or decreasing. If there is more than one interval, enter your intervals from left to right as they appear on the real line. Enter INF for 00 and -INF for-00 If there are extra blanks, enter NONE. Increasing: (-1/2,1/2), (NONE, NONE) You are correct. Your receipt no. is 152-6082 Previous Tries Decreasing: ((1/2) , NONE new INF NONE Submit Answer Incorrect. Tries 6/99 Previous Tries Apply the First Derivative Test to find the relative extrema if they exist. Enter your answer in the format of (x, y). If not, enter NONE in the blanks. Relative Maximum: (1/2,7) You are correct. Your receipt no. is 152-9742 Relative Minimum: -1/2,3) You are correct. Your receipt no. is 152-5334

Answer 1

y = 5 + 6 x - 8 x^3 dy/dx = 6 - 24 x^2 dy/dx = 0 implies 6(1 - 4 x^2) implies 6(1 - 2x) (1 + 2x) = 0 implies x = plusminus 1/2 dy/dx > 0 implies 6(1 - 2x) (1 + 2x) > 0 implies 1 - 2x > 0 & 1 + 2x > 0 (or) (1 - 2x) < 0 & (1 + 2x) < 0 1 - 2x > 0 & 1 + 2x > 0 x < 1/2 & x > -1/2 (1 - 2x) < 0 & (1 + 2x) < 0 2x > notepsilon 1 & x < 1/2 x > 1/2 & x < 1/2 & x < 1/2 no intersection. Implies (-1/2, 1/2) implies fn is increasing on (-1/2, 1/2) dy/dx < 0 implies (1 - 2x) < 0 & (1 + 2x) > 0 2x > 1 & 2x > -1 x > 1/2 x > -1/2 x belongsto (1/2, infinity) \r\n (or) (1 - 2x) > 0 &