(4) A closed rectangular container with a square base is to have a volume of 2250in². for the top and bottom of the container will cost $2 per in², and the cost $3 per in2. Find the dimensions of the container of lest cost. The material material for the sides will
(4) A closed rectangular container with a square base is to have a volume of 2250in². for the top and bottom of the container will cost $2 per in², and the cost $3 per in2. Find the dimensions of the container of lest cost. The material material for the sides will
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![(4) A closed rectangular container with a square base is to have a volume of 2250in². The material
for the top and bottom of the container will cost $2 per in², and the material for the sides will
cost $3 per in2. Find the dimensions of the container of lest cost.
(5) Let s(t) = t³ - 9t2 +24t be the position function of a particle moving along a coordinate line
where s is in meters and t is in minutes.
(a) Find the velocity and acceleration functions,
(b) Find the position, velocity, speed, and acceleration at time t = 1
(c) At what time is the particle stopped?
(d) When is the particle speeding up? Slowing down?
(e) Give a schematic picture of the motion,
(f) Find the maximum speed of the particle during the time interval 0 < t < 5,
(g) Find the total distance traveled by the particle from time t = 0 to t=5.
(6) Verify that each function satisfies the hypothesis of the Mean Value Theorem on the interval
[a, b]. Then find all the numbers c that satisfy the conclusion of the Mean Value Theorem.
(a) f(x)=1-√√r-1 on [2,10],
(b) g(x) = x³ + x -4 on [-1,2]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fba01848d-09ed-47b0-8866-1aec132e3933%2Ff50b291b-cbdf-486c-b054-98e6db93930d%2Futtg2w_processed.jpeg&w=3840&q=75)
Transcribed Image Text:(4) A closed rectangular container with a square base is to have a volume of 2250in². The material
for the top and bottom of the container will cost $2 per in², and the material for the sides will
cost $3 per in2. Find the dimensions of the container of lest cost.
(5) Let s(t) = t³ - 9t2 +24t be the position function of a particle moving along a coordinate line
where s is in meters and t is in minutes.
(a) Find the velocity and acceleration functions,
(b) Find the position, velocity, speed, and acceleration at time t = 1
(c) At what time is the particle stopped?
(d) When is the particle speeding up? Slowing down?
(e) Give a schematic picture of the motion,
(f) Find the maximum speed of the particle during the time interval 0 < t < 5,
(g) Find the total distance traveled by the particle from time t = 0 to t=5.
(6) Verify that each function satisfies the hypothesis of the Mean Value Theorem on the interval
[a, b]. Then find all the numbers c that satisfy the conclusion of the Mean Value Theorem.
(a) f(x)=1-√√r-1 on [2,10],
(b) g(x) = x³ + x -4 on [-1,2]
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