# Find the absolute maximum and absolute minimum values

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Find the absolute maximum and absolute minimum values of f on the given interval. f ( x ) = 6 x 3 18 x 2 144 x + 4 , [ −3 , 5 ] Part 1 of 4 The absolute maximum and minimum values of f occur either at a critical point inside the interval or at an endpoint of the interval. Recall that a critical point is a point where f ' ( x ) = 0 or is undefined. We begin by finding the derivative of f . f ' ( x ) = \$\$18 x 2−36 x −144 Part 2 of 4 We now solve f ' ( x ) = 0 for x , which gives the following critical numbers. (Enter your answers as a comma-separated list.) x = \$\$−2, 4 Part 3 of 4 We must now find the function values at the critical numbers we just found and at the endpoints of the interval [ −3 , 5 ]. f ( −2 ) = 3172 f ( 4 ) = 4-476 f ( −3 ) = 5112 f ( 5 ) = 6-416 Part 4 of 4
Therefore, on the interval [ −3 , 5 ], the absolute minimum of f ( x ) is \$\$−476 and the absolute maximum is \$\$172 . You have now completed the Master It. 0 Viewing Saved Work Revert to Last Response 11. 2/2 points | Previous Answers My Notes Question Part Points Submissions Used 1 2 1/1 1/1 3/5 1/5 A tennis ball is dropped from a height of 10 feet at time t=0 seconds. For the next seconds, its height above the ground is modeled by the function: Practice Another Version
(b) The t input when the maximum value of h(t) occurs:
Viewing Saved Work Revert to Last Response 12. 12/12 points | Previous Answers My Notes Question Part Points Submissions Used 1 2 3 4 3/3 3/3 3/3 3/3 1/5 1/5 1/5 3/5 Total 12/12 Consider an object moving along the parametrized curve with equations: x(t)= e t + e t , y(t)= e t where t is in the time interval [ 0 , 7 ] seconds. (a) The maximum speed of the object on the time interval is \$\$1096.632 at time \$\$7 . (b) The minimum speed of the object on the time interval is \$\$0.910 Practice Another Version
at time \$\$ ln (2)4 Viewing Saved Work Revert to Last Response Home My Assignments WebAssign® 4.0 © 1997-2016 Advanced Instructional Systems, Inc. All rights reserved. Practice Another Version