Question

Homework14: Problem 13 Previous Problem Problem List Next Poblem (1 point) Let f(x) = – 4 – 579 +6 +5. Find the open intervals on which fis concave up (down) Then determine the so-coordinates of all inflection points off f is concave up on the intervals 2. f is concave down on the intervals The inflection points occur at 1. 3. Notes: In the first two your answer should either be a single interval, such as (0,1), a comma separated list of intervals, such as (-inf 2), (3,4), or the word "none" In the last one, your answer should be a comma separated list of values of the word "none" Note: You can earn partial credit on this problem, Preview My Answers Submit Answers You have attempted this islam times BI search

Answer 1

f(x) = -44 - 5x3 +68+5 An inflection point is a point on the graph at which the second derivative changes sign. if + "(x) so then f(a) concave upwards if f(x) TO then f(x) concame downwards. Now . - 4x²_15x²+6 f"(a) -12 x ² - -360 t"(*) -12x2 - 30x = 0 x=0, x= -5/ so f (x) sign interval will be (-2,-52), 692,0), (0, 0) Check the sign of f(x) in each internal - La L-5/ - 5/2 <aco x x sign s. t is concave up on the interual (-5%,0) of is concave down on the interval (0, -S/2) U (0,0) The inflection point occur at a = + 2. -5/20 3.