Answer Key
799
3.29 . f ′( x ) =2sec 2 x +3csc 2 x 3.30 . 4 3 3.31 . cos x 3.32 . −cos x 3.33 . v ⎛ ⎝ 5 π 6 ⎞ ⎠ =− 3<0 and a ⎛ ⎝ 5 π 6 ⎞
⎠ =−1<0. The block is speeding up.
3 ⎛
3
3.34 . h ′( x ) =4 ⎛
⎝ 2 x 3 +2 x −1 ⎞ ⎠
⎛ ⎝ 2 x 3 +2 x −1 ⎞ ⎠
⎝ 6 x 2 +2 ⎞
⎛ ⎝ 3 x 2 +1 ⎞ ⎠
⎠ =8
3.35 . y =−48 x −88 3.36 . h ′( x ) =7cos(7 x +2) 3.37 . h ′( x ) = 3−4 x (2 x +3) 4 3.38 . h ′( x ) =18 x 2 sin 5 ⎛ ⎝ x 3 ⎞
⎛ ⎝ x 3
⎞ ⎠
⎠ cos
3.39 . a ( t ) = −16sin(4 t ) 3.40 . 28 3.41 . dy dx =−3 x 2 sin ⎛ ⎝ x 3 3.42 . g ′( x ) = − 1
⎞ ⎠
( x +2) 2
3.43 . g ( x ) = 1 5 x −4/5 3.44 . s ′( t ) = (2 t +1) −1/2 3.45 . g ′( x ) = 1 1+ x 2 3.46 . h ′( x ) = −3 6 x −9 x 2 3.47 . y = x 3.48 . dy dx = 5−20 x 4 sec 2 y −2 y 3.49 . y = 5 3 x − 16 3 3.50 . h ′( x ) = e 2 x +2 xe 2 x 3.51 . 996 3.52 . f ′( x ) = 15 3 x +2 3.53 . 9ln(3) 3.54 . dy dx = x x (1+ln x ) 3.55 . y ′ = π (tan x ) π −1 sec 2 x Section Exercises 1 . 4
3 . 8.5 5 . − 3 4 7 . 0.2 9 . 0.25
11 . a. −4 b. y =3−4 x 13 . a. 3 b. y =3 x −1
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