Question

Consider the following graph.
The x y coordinate plane is given. The curve begins at (0, 5) goes down and right becoming less steep, changes direction at (1, 2) goes up and right becoming more steep, goes through the approximate point (2, 3.1), goes up and right becoming less steep, changes directions at (3, 4), goes down and right becoming more steep, sharply changes direction at (4, 1), goes up and right becoming less steep passing through the approximate point (5, 4.2) and ends at (6, 6).
(a) Find the interval(s) on which f is increasing. (Enter your answer using interval notation.)
(b) Find the interval(s) on which f is decreasing. (Enter your answer using interval notation.)
(c) Find the open interval(s) on which f is concave upward. (Enter your answer using interval notation.)
(d) Find the interval(s) on which f is concave downward. (Enter your answer using interval notation.)
(e) Find the coordinates of the point(s) of inflection.
(x, y) = ( )

Answer 1

a)Function is increasing in intervals (1,3) and (4,6).

b)Function is decreasing in intervals (0,1) and (3,4).

c)Graph is concave upward in the interval (0,2) and (3,5).

d)Graph is concave downward in the interval (3,4).

e)Points of inflection are x=3 and x=5.

Let us make the graph of the given function. In the graph, We have connected points linearly, please consider it as a curve.

What is the point of inflection?

The point of inflection or inflection point is a point in which the concavity of the function changes.

Therefore, From the attached graph, we can see that:

a)Function is increasing in intervals (1,3) and (4,6).

b)Function is decreasing in intervals (0,1) and (3,4).

c)Graph is concave upward in the interval (0,2) and (3,5).

d)Graph is concave downward in the interval (3,4).

e)Points of inflection are x=3 and x=5.

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