Question

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].

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).