Is #f(x)=-x^5-2x^4+8x^2-4x+2# concave or convex at #x=-5#?
1 Answer
Feb 23, 2016
convex at x = -5
Explanation:
To test if a function is concave / convex at f(a) , require to find the value of f''(a).
• If f''(a) > 0 then f(x) is convex at x = a
• If f''(a) < 0 then f(x) is concave at x = a
hence
#f(x) = -x^5 -2x^4 +8x^2 - 4x + 2#
#f'(x) = -5x^4 - 8x^3 + 16x - 4# and
#f''(x) = -20x^3 - 24x^2 + 16#
#rArr f(-5) - -20(-5)^3 - 24(-5)^2 + 16 = 1916# since f''(-5) > 0 then f(x) is convex at x = -5
