Question
In each part below, sketch a graph of a function whose domain is [0, 4] that...
In each part below, sketch a graph of a function whose domain is [0, 4] that has the desired property. No justification is needed in any part.
(a) f(x) has an absolute maximum and absolute minimum on [0, 4].
(b) g(x) has neither an absolute maximum nor an absolute minimum on [0, 4].
(c) h(x) has exactly two local minima and one local maximum on [0, 4].
(d) k(x) has one inflection point and no local extrema on [0, 4].
Homework Answers
Answer #1
a)
On the interval [0,4], the absolute minimum value of f(x) is -5 at x = 0.
On the interval [0,4], the absolute maximum value of f(x) is 4 at x = 3.
Below is the graph of the function f(x).
b)
On the interval [0,4], g(x) has no absolute maximum and absolute minimum value as seen in the below graph.
c.
On the interval [0,4], h(x) has two local minima at x = 1 and x = 3 respectively.
On the interval [0,4], h(x) has one local maximum at x = 2.
Below is the graph of the function h(x).
d.
On the interval [0,4], k(x) has one inflection point at x = 2 and no local extrema.
Below is the graph of the function k(x).
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