Is #f(x)=-x^3-x^2+x# concave or convex at #x=4#?
1 Answer
Mar 22, 2016
concave at x = 4
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^3 - x^2 + x # f'(x) =
#-3x^2 - 2x + 1# and f''(x) = -6x -2
hence : f''(4) = -6(4) - 2 = - 26
since f''(4) < 0 then f(x) is concave at x = 4
