Is #f(x)=-x^3-12x^2-14x-2# concave or convex at #x=0#?
1 Answer
Concave at
Explanation:
The test for convexity/concavity is to check the value of the 2nd derivative
• If
#f''(0) > 0# then convex at#x = 0# • If
#f''(0) < 0# then concave at#x = 0#
Find the 2nd derivative :
#f(x) = - x^3 -12x^2 - 14x -2#
#f'(x) = -3x^2 -24x - 14#
#f''(x) = 6x - 24#
Now
Hence