Is f(x)=4x^5+2x^3-2x^2+2x+8f(x)=4x5+2x3−2x2+2x+8 concave or convex at x=-3x=−3?

1 Answer
Jim G.
May 8, 2016

concave at x = -3

Explanation:

To determine if a function is concave/convex at f(a) we 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)=4x^5+2x^3-2x^2+2x+8f(x)=4x5+2x3−2x2+2x+8

rArr f'(x)=20x^4+6x^2-4x+2

and f''(x)=80x^3+12x-4

rArrf''(-3)=80(-3)^3+12(-3)-4=-2200

Since f''(-3) < 0 , then f(x) is concave at x = -3

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