Is #f(x)=x^3-2x+7 # concave or convex at #x=2 #?
1 Answer
Sep 25, 2016
convex at x = 2
Explanation:
To determine if a function f(x) is concave/convex at x = 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
Now
#f(x)=x^3-2x+7# differentiate using the
#color(blue)"power rule"#
#rArrf'(x)=3x^2-2# and
#f''(x)=6x#
#rArrf''(2)=(6xx2)=12# Since f''(2) > 0 then f(x) is convex at x = 2.
graph{x^3-2x+7 [-22.5, 22.5, -11.25, 11.25]}
