Is #f(x)=4x^5+2x^3-2x^2+2x+8# concave or convex at #x=-3#?
1 Answer
May 8, 2016
concave at x = -3
Explanation:
To determine if a function is concave/convex at f(a) we 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)=4x^5+2x^3-2x^2+2x+8#
#rArr f'(x)=20x^4+6x^2-4x+2# and
#f''(x)=80x^3+12x-4#
#rArrf''(-3)=80(-3)^3+12(-3)-4=-2200# Since f''(-3) < 0 , then f(x) is concave at x = -3
