Solução_Calculo_Stewart_6e

F.
TX.10
SECTION 4.5 SUMMARY OF CURVE SKETCHING ¤ 177
29. y = f(x) = 3√ x 2 − 1 A. D = R B. y-intercept: f(0) = −1; x-intercepts: f(x) =0 ⇔ x 2 − 1=0 ⇔
x = ±1 C. f(−x) =f(x), so the curve is symmetric about the y-axis. D. No asymptote
E. f 0 (x) = 1 3 (x2 − 1) −2/3 (2x) =
increasing on (0, ∞) and decreasing on (−∞, 0).
G. f 00 (x)= 2 3 · (x2 − 1) 2/3 (1) − x · 2
3 (x2 − 1) −1/3 (2x)
[(x 2 − 1) 2/3 ] 2
2x
3 3 (x 2 − 1) 2 . f 0 (x) > 0 ⇔ x>0 and f 0 (x) < 0 ⇔ x 0 ⇔ −1 0 ⇔ x ∈ 2nπ − π , 2nπ + π
2 2 for each integer n, andf 0 (x) < 0 ⇔ cos x0 and sin x 6=±1 ⇔ x ∈
2nπ, 2nπ + π 2 ∪ 2nπ +
π
, 2nπ + π for some integer n.
2
f 00 (x) > 0 ⇔ sin x