Determine the relative maximum and minimum on the graph

[Jay007]

Given that f is the function on (−∞, ∞) and the graph is the derivative of f

1.) Find the critical point on the graph ?
2.) Find the interval of the increasing function on the graph ?
3.) Find the interval of the decreasing function on the graph ?
4.) Find the point which is the relative maximum on the graph ?
5.) Find the point which is the relative minimum on the graph ?



My answers for all of the question that I have done on my own is

• 1.) 4.5,13
• 2.) [0,4.5] , (10,13]
• 3.) [4.5,10), [13, - ∞)
• 4.) 4.5,13
• 5.) 10

I want to check that I am doing it correct or not because I am not good at discontinuous graph
Can you please help me
Thank you in advice

 

[Eduleo]

My english is not very good... The questions refers to the original function or to the graphed one (the derivative)? That is, you are expected to find the critical points, increasing/decreasing ranges, max/min points of the orginal function "f" based on the graph of his derivative (f'), or is about the last one or a mix of both?

 

[pka]

Given that f is the function on (−∞, ∞) and the graph is the derivative of f

1.) Find the critical point on the graph ?
2.) Find the interval of the increasing function on the graph ?
3.) Find the interval of the decreasing function on the graph ?
4.) Find the point which is the relative maximum on the graph ?
5.) Find the point which is the relative minimum on the graph ?

View attachment 21458

My answers for all of the question that I have done on my own is

• 1.) 4.5,13
• 2.) [0,4.5] , (10,13]
• 3.) [4.5,10), [13, - ∞)
• 4.) 4.5,13
• 5.) 10

I want to check that I am doing it correct or not because I am not good at discontinuous graph
Can you please help me
Thank you in advice

There are problems with the question itself. There is no universal agreement on what a critical point is.
Almost all agree that \(x=4.5~\&~x=13\) are critical points being relative maxima.
However, many authors would insist that \(x=2,~x=7,~\&~x=10\) are also critical because they are inflection points, SEE HERE
Some authors will insist that \(x=10\) is critical because the function is not defined there.
So you must follow the textbook in use.

 

[Steven G]

It seems that you answered the question as if you were given the graph of f (and you had a few mistakes). However you were given the graph of f'. Please try again.

Since you had some mistakes assuming you were given the graph of f(x) I think that I should point out your errors.
#1 is not a complete list. A critical point is an x value which makes the derivative 0 or undefined. You misses x=10.
#4 The question should say to find the point(s) which is (are) the relative max on the graph! Your answer is NOT correct as you failed to write points. You may have written the correct x-values but that is not a point!
#5 How can x=10 (again NOT a point!) be the x-value of the relative min when the graph is NOT even defined at x=10? In this graph there is NO relative min. Do you see that?

 

[Dr.Peterson]

My english is not very good... The questions refers to the original function or to the graphed one (the derivative)? That is, you are expected to find the critical points, increasing/decreasing ranges, max/min points of the original function "f" based on the graph of his derivative (f'), or is about the last one or a mix of both?

I think the difficulty is not your English, but the English used by the author of the problem, which is very poorly stated!

It clearly tells us that the graph is of f'; but then it keeps asking for the critical points, etc., on the graph, not of the function. I really don't know which is intended!

But I would expect it to mean, the critical points of the function, based on the graph.

Furthermore, everything is in the singular, when in fact (either way we take it) there are multiple critical points, multiple intervals of increase, etc.

And finally (unless I'm missing some issues), if it is asking about f rather than the graph, we can't find max or min points, which would require knowing values of the function f, which we don't have. We could only find the x-coordinates.

 

[Steven G]

I think the difficulty is not your English, but the English used by the author of the problem, which is very poorly stated!

It clearly tells us that the graph is of f'; but then it keeps asking for the critical points, etc., on the graph, not of the function. I really don't know which is intended!

But I would expect it to mean, the critical points of the function, based on the graph.

Furthermore, everything is in the singular, when in fact (either way we take it) there are multiple critical points, multiple intervals of increase, etc.

And finally (unless I'm missing some issues), if it is asking about f rather than the graph, we can't find max or min points, which would require knowing values of the function f, which we don't have. We could only find the x-coordinates.

Yes yes, you are correct. They asked for the critical points, etc of the graph.