Is f(x)=-x^5-2x^4+8x^2-4x+2 concave or convex at x=-5?

1 Answer
Feb 23, 2016

convex at x = -5

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 -2x^4 +8x^2 - 4x + 2

f'(x) = -5x^4 - 8x^3 + 16x - 4

and f''(x) = -20x^3 - 24x^2 + 16

rArr f(-5) - -20(-5)^3 - 24(-5)^2 + 16 = 1916

since f''(-5) > 0 then f(x) is convex at x = -5