Is #f(x)=-x^5-x^4-2x^3+x-7# concave or convex at #x=-2#?
1 Answer
Mar 6, 2016
convex at x = -2
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 - x^4 - 2x^3 + x - 7# f'(x)
# = -5x^4 - 4x^3 - 6x^2 + 1# and f''(x)
# = -20x^3 - 12x^2 - 12x#
#rArr f''(-2) = -20(-2)^3 - 12(-2)^2 - 12(-2)# = 160 - 48 + 24 = 136
since f''(-2) > 0 then f(x) is convex at x = -2
graph{(-x^5-x^4-2x^3+x-7) [-16.02, 16.02, -8.01, 8.01]}
