Question

Consider the function below. (If you need to use -- or, enter -INFINITY or INFINITY.) C(x) = x1/5(x + 6) (a) Find the interval of increase. INFINITY Find the interval of decrease. ( INFINITY ) (b) Find the local minimum value. -5 (c) Find the inflection points. (Give your answers correct to one decimal place.) (smaller x value) X ) (larger x value) (o 0 Find the intervals where the function is concave up. (Enter the interval that contains smaller numbers first.) ( INFINITY 0 UCI X , INFINITY ) Find the interval where the function is concave down. (

Answer 1

1/5 [ (x) (x+6) 6 (2+1) © C'(X) = 4/55 52 6 (-4) c" (X) = 9/5 Put C"(x) = 0 For inflection point 6 (2-4) 9/5 250 x=0 2= 4

Put x=0 1/5 = 0 C (0) = (0) (0+6) - [0,0] Put X= 4 Is C (4) - (4) (6+4) C (4) = 10 (4) 13.19 C (4) = [ 4, 13.19 J

@ Concave up 6 (x-4) c"(2 = 214 1 [-20 <x< 0] put = (1-),,? 6(1-4) 25 (-13°74 Positive

C" (20) = 6 (2-4) 9/4 [ 4<x500] 25 x Put 2= 15 c" (15) 6 (5-4) 25 (5) 914 Positive Concave Up [-00, 0] U [ [4,00) Concave Downward 6 (2-4) [0<x<4] 914 c" () = 25 Put x=2 (" (2) - 6 (2-4) 25 (2) 914 Negative concave Down [0,4