x gall 2 agiel Jual x webwork petroleumi x C Chegg Study I Guided so x YouTube C
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x gall 2 agiel Jual x webwork petroleumi x C Chegg Study I Guided so x YouTube C a Secure https:// webwork maa org 111/Hw 7-3 3.3/8/? user 8736&effectiveUser; 8736&key; GtK5NE0bWIEu JWCm JNnjGzve2eTtHHDc tr E3 S E Apps Getting Started D New Tab Logged in as 8736. Log Out MATHEMATICAL ASSOCIATION OF AMERICA K webwork petr euminst-math 111 hw 7-3.1 3.3 8 MAIN MENU Courses Homework Sets Hw 7-3.1 3.3: Problem 8 Hw 7-3,1 3.3 Problem 8 Previous Problem List Next User Settings Grades 1 point) Let f(z) -a 4 8z3 2z 8. Find the open intervals on which f s concave up (down). Then determine the z-coordinates of all inflection points of f Problems 1. f is concave up on the intervals 2. f s concave down on the intervals Problem 1 3. The infection points occur at Problem 2 Problem 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 Problem the word "none". Problem 5 In the last one, your answer should be a comma separated list of 2 values or the word "none". Problem 6 Problem 7 Problem 8 Note: You can eam partial credit on this problem. Problem 9 Preview My Answers Submit Answers Problem 10 You have attempted this problem 0 times. You have unlimited attempts remaining. Ema nstructor webwork maa.org/webwork2/petroleumin meth 3.3/8/?ef 9:32 PM NG 3/1S2017Explanation / Answer
f(x) = -x^4 - 8x^3 +2x -8
f '(x) = -4x^3 - 24x^2 +2, but
this is the FIRST derivative, not the second derivative.
f "(x) =-12x^2 - 48x
The inflection points can occur only where f''(x) = 0
==> -12x^2 - 48x =0
==> x^2 + 48x =0
===> x ( x + 48 ) = 0
===> x=0 , x = - 48
the inflection points are at 0 and -48
Note that f(0) =-8 , and that when x is large (either positive or negative),
the value of f approaches 0.
Thus, f is concave down on (-48,0);
it is concave upward on (-infinity, -48) and also on (0, +infinity).
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