Is #f(x)=-9x^5+15x^4-21x^2-8x+2# concave or convex at #x=3#?
1 Answer
Feb 13, 2016
concave at x = 3
Explanation:
To test for concavity/convexity , require to evaluate f''(x).
• If f''(x) > 0 then f(x) is convex
• If f''(x) < 0 then f(x) is concave
require to find f''(x) and then value of f''(3)
# f'(x) = - 45x^4 + 60x^3 - 42x - 8#
# f''(x) = -180x^3 + 180x^2 - 42#
#f''(3) = -180(3)^3 + 180(3)^2 -42 # = -4860 + 1620 - 42 = - 3282 < 0
since f''(3) < 0 then f(x) is concave at x = 3
