1) Explain the differences between an absolute minimum and a local minimum.

College Algebra (MindTap Course List)
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Author:R. David Gustafson, Jeff Hughes
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Chapter3: Functions
Section3.3: More On Functions; Piecewise-defined Functions
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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) = V? – t
%3D
%3D
(d) f(x) = xe²-
(e)g(x) = x ln
%3D
4) Find the absolute ma
mum and absolute minimum values
f on the given interval.
(a)f(x) = 3x2 – 12x + 5 on the interval [0, 3]
(b) f(x) = x – In x, on the interval [, 2]
Transcribed Image Text: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) = V? – t %3D %3D (d) f(x) = xe²- (e)g(x) = x ln %3D 4) Find the absolute ma mum and absolute minimum values f on the given interval. (a)f(x) = 3x2 – 12x + 5 on the interval [0, 3] (b) f(x) = x – In x, on the interval [, 2]
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