{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Homework5

# Homework5 - MA 115 Homework Solutions for Week 5 4.2#6...

This preview shows pages 1–2. Sign up to view the full content.

MA 115 Homework Solutions for Week 5 4.2 #6 Absolute maximum value is f (8) = 5; absolute minimum value is f (2) = 0; local maximum values are f (1) = 2, f (4) = 4, and f (6) = 3; local minimum values are f (2) = 0, f (5) = 2, and f (7) = 1. 4.2 #24 f ( x ) = x 3 + x 2 x f ( x ) = 3 x 2 + 2 x 1 f ( x ) = 0 ( x + 1)(3 x 1) = 0 x = 1 , 1 3 . These are the only critical numbers. 4.2 #38 f ( x ) = x 3 3 x + 1 , [0 , 3]. f ( x ) = 3 x 2 3 = 0 x = ± 1, but 1 / [0 , 3]. So by testing the values x = 0 , 1 , 3 we see f (0) = 1, f (1) = 1 and f (3) = 19. So f (3) = 19 is the absolute maximum value and f (1) = 1 is the absolute minimum value. 4.2 #46 f ( x ) = x 2 cos x, [ π, π ]. f ( x ) = 1+2 sin x = 0 sin x = 1 2 x = 5 π 6 , π 6 . By comparing the function value at both endpoints and the critical points we see f ( π ) = 2 π ≈ − 1 . 14, f ( 5 π 6 ) = 3 5 π 6 ≈ − 0 . 886, f ( π 6 ) = π 6 3 ≈ − 2 . 26, f ( π ) = π + 2 5 . 14. So f ( π ) = π + 2 is the absolute maximum value and f ( π 6 ) = π 6 3 is the absolute minimum value. 4.3 #6 (a) f is increasing on the intervals where f ( x ) > 0, namely, (2 , 4) and (6 , 9). (b) f has a local maximum where it changes from increasing to decreasing, that is, where f changes from positive to negative (at x = 4). Similarly, where f changes from negative to positive, f has a local minimum (at x = 2 and at x = 6). (c) When f is increasing, its derivative f ′′ is positive and hence, f is concave upward. this happens on (1 , 3) , (5 , 7) and (8 , 9). Similarly, f is concave downward when f is decreasing–that is, on (0 , 1) , (3 , 5) and (7 , 8).

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 5

Homework5 - MA 115 Homework Solutions for Week 5 4.2#6...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online