Solução_Calculo_Stewart_6e

F.
TX.10
SECTION 4.5 SUMMARY OF CURVE SKETCHING ¤ 173
5. y = f(x) =x 4 +4x 3 = x 3 (x +4) A. D = R B. y-intercept: f(0) = 0;
H.
x-intercepts: f(x) =0 ⇔ x = −4, 0 C. No symmetry
D. No asymptote E. f 0 (x) =4x 3 +12x 2 =4x 2 (x +3)> 0 ⇔
x>−3,sof is increasing on (−3, ∞) and decreasing on (−∞, −3).
F. Local minimum value f(−3) = −27, no local maximum
G. f 00 (x) =12x 2 +24x =12x(x +2)< 0 ⇔ −2 1,sof is CU on (1, ∞) and
(x − 1)
3
11. y = f(x) =1/(x 2 − 9) A. D = {x | x 6=±3} =(−∞, −3) ∪ (−3, 3) ∪ (3, ∞) B. y-intercept = f(0) = − 1 9 ,no
1
x-intercept C. f(−x) =f(x) ⇒ f is even; the curve is symmetric about the y-axis. D. lim =0,soy =0
x→±∞ x 2 − 9
is a HA.
1
1
lim = −∞, lim
x→3 − x 2 − 9 x→3 + x 2 − 9 = ∞,
lim 1
x→−3 − x 2 − 9 = ∞,
lim 1
= −∞, sox =3and x = −3
x→−3 + x 2 − 9
are VA. E. f 0 2x
(x) =−
(x 2 2
> 0 ⇔ x