Question

7. List the intervals of concavity and the inflection point(s) for the following function. If there are none write NA. f(x) = x4 – 4x3 Intervals on which f is Concave Up: Intervals on which f is Concave Down: Inflection Point(s) (ordered pair):_

Answer 1

SOLUTION. fla x" 4x² for concauity and inflection pointis we first need to find f"(n) t(a) 4x²_ 12x² f"(wwa 125- 24% put f"(0) = 0 for inflection point (4) 12x?- 24% =0 12x (x - 2) =0 x = 2 Inflection points, > concave up for f"(7) > 0 12x²- 24x 12x (1-2) >O >0 ) + 24 - 0 7-2 f"Carlo f is concave up in (-0,0U (2.0) f is concave down for 127 (x-2) 20 f is con came down in (0, 2) concowe (0,2) Interwals on which f is up : (-2,0) U (2.00) Internals on which f is concave down: Inflection points : (o, fco)) (2,-16) (0,0) 12, f(2))