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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can you please answer number 5
![2021
4.1 Related Rates:
# 1) If V is the volume of a cube with edge length x and the cube expands as time passes,
find dV/dt in terms of dx/dt.
# 3) Each side of a square is increasing at a rate of 6cm/s. At what rate is the area of
the square increasing when the area of the square is 16cm?.
# 5) If y = x³ + 2x and dx/dt = 5, find dy/dt when x = 2.
# 9) If a snowball melts so that its surface area decreases at a rate of lcm² /min, find the
rate at which the diameter decreases when the diameter is 10cm.
# 10) At noon ship A is 150 km west of ship B. Ship A is sailing east at 35km/h and
ship B is sailing north at 25km/h. How fast is the distance between the ships changing at
4: 00 P.M.?
4.2 Maximum and Minimum Values:
1) Explain the differences between an absolute minimum and a local minimum.
2) Sketch the graph of a function f that is continuous on [1,5] such that f has absolute
minimum at 3, absolute maximum at 5, local maximum at 2 and local minimum at 4.
3) Find the critical numbers of the following functions.
(a)f(x) = 5x² + 4x
(b)f(x) =
= x³ + x² – x
(c)f(t) = V² – t
(d)f(x) = xe²¤
(e)g(x) = x ln x
4) Find the absolute maximum and absolute minimum values of f on the given interval.
(a)f(x) = 3x² – 12.x + 5 on the interval [0, 3]
(b) f(x) = x – In x, on the interval [, 2]
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Transcribed Image Text:2021
4.1 Related Rates:
# 1) If V is the volume of a cube with edge length x and the cube expands as time passes,
find dV/dt in terms of dx/dt.
# 3) Each side of a square is increasing at a rate of 6cm/s. At what rate is the area of
the square increasing when the area of the square is 16cm?.
# 5) If y = x³ + 2x and dx/dt = 5, find dy/dt when x = 2.
# 9) If a snowball melts so that its surface area decreases at a rate of lcm² /min, find the
rate at which the diameter decreases when the diameter is 10cm.
# 10) At noon ship A is 150 km west of ship B. Ship A is sailing east at 35km/h and
ship B is sailing north at 25km/h. How fast is the distance between the ships changing at
4: 00 P.M.?
4.2 Maximum and Minimum Values:
1) Explain the differences between an absolute minimum and a local minimum.
2) Sketch the graph of a function f that is continuous on [1,5] such that f has absolute
minimum at 3, absolute maximum at 5, local maximum at 2 and local minimum at 4.
3) Find the critical numbers of the following functions.
(a)f(x) = 5x² + 4x
(b)f(x) =
= x³ + x² – x
(c)f(t) = V² – t
(d)f(x) = xe²¤
(e)g(x) = x ln x
4) Find the absolute maximum and absolute minimum values of f on the given interval.
(a)f(x) = 3x² – 12.x + 5 on the interval [0, 3]
(b) f(x) = x – In x, on the interval [, 2]
1
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