Calculus Volume 1

Answer Key

827

515 . F ( x ) = 1 3 x 3 +2 x 517 . F ( x ) = x 2 −cos x +1 519 . F ( x ) = − 1 ( x +1) +1

521 . True 523 . False Review Exercises 525 . True, by Mean Value Theorem 527 . True 529 . Increasing: (−2, 0) ∪ (4, ∞), decreasing: (−∞, −2) ∪ (0, 4) 531 . L ( x ) = 17 16 + 1 2 (1+4 π ) ⎛ ⎝ x − 1 4 ⎞ ⎠

533 . Critical point: x = 3 π

x =0, absolute maximum: x = π

4 , absolute minimum: (−1, 0) ∪ (3, ∞),

(−∞, −1) ∪ (0, 3),

535 .

Increasing:

decreasing:

concave

up:

⎛ ⎝ −∞, 1 3 ⎛

⎝ 2− 13 ⎞ ⎠ ⎞

⎛ ⎝ 1 3

⎞ ⎠ , concave down:

⎛ ⎝ 1 3

⎞ ⎠

⎛ ⎝ 2+ 13 ⎞

⎛ ⎝ 2− 13 ⎞

⎛ ⎝ 2+ 13 ⎞ ⎠

⎠ ∪

⎠ , ∞

⎠ , 1 3

⎛ ⎝ 1

⎞ ⎠ , decreasing:

⎛ ⎝ 0, 1 4

⎞ ⎠ , concave up: (0, ∞), concave down: nowhere

537 . Increasing:

4 , ∞

539 . 3 541 . − 1 π 543 . x 1 =−1, x 2 =−1 545 . F ( x ) = 2 x 3/2 3 + 1

x + C

547 .

Inflection points: none; critical points: x = − 1

x =−1, x =0; horizontal asymptote:

3 ; zeros: none; vertical asymptotes:

y =0 549 . The height is decreasing at a rate of 0.125 m/sec 551 . x = ab feet Chapter 5 Checkpoint 5.1 . ∑ i =3 6 2 i =2 3 +2 4 +2 5 +2 6 =120 5.2 . 15,550 5.3 . 440 5.4 . The left-endpoint approximation is 0.7595. The right-endpoint approximation is 0.6345. See the below image .

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