determining equation from given info...

[mattttt]

hello and thanks ahead of time!!!

here is the problem

In the following problem, f(x) is continuous and has derivatives everywhere. there are no boundar points. use the info below to determine whether x-coordinate 5 is a local max, local min, inflection point, or none of the above. there are no other critical points close to x=5.

f ' (5)=0
f ' (4)=-2
f ' (6)=2

........ my issue is i am not sure how to to come up with the equation needed to determine what x=5 is.......... all of the study materials i have explain how to answer the question if i had an equation, but i do not....

any input is appreciated!!

 

[stapel]

i am not sure how to to come up with the equation needed to determine what x=5 is.

I'm afraid I don't know what you mean by "what x = 5 is"...? Also, I don't see anywhere in the exercise where you have been instructed to "come up with the equation"...? (I don't believe such would even be possible, and is certainly not possible with only the information provided thus far.)

Instead, try considering the information included within the exercise. You are given the value of the derivative in three locations. Use what you have learned about slopes, derivatives, max/min points, and grphing. What do these values say about the slope at these various points, and the general shape of the function in that area? And so forth.

Eliz.

 

[mmm4444bot]

... determine whether x-coordinate 5 is a local max, local min, inflection point, or none of the above ...

Are you the author of the sloppy instruction above? (This is a rhetorical question.)

The instruction properly written follows.

"Determine whether the behavior of function f at x = 5 is a local maximum, a local minimum, an inflection point, or none of these."

Mattttttttttttttttttt, do you know? The first derivative of a function gives the slope of that function's graph.

Do you know? If the slope of a continuous function's graph changes sign, then there must be a local minimum or maximum.

If we're told that f'(4) = -2, then we know that the slope of the graph of f is -2 at the point where the x-coordinate is four.

If we're told that f'(6) = 2, then we know that the slope of the graph of f is 2 at the point where the x-coordinate is six.

If you do not understand these things, then please let us know because you will not be able to complete this exercise.

-

... my issue is i am not sure how to to come up with the equation needed ...

No equation is needed to complete this exercise because this exercise is not asking you to calculate any numbers.

The real issue may be that you do not understand the exercise. This exercise is CONCEPTUAL. (Do you know what this means?)

Here's the way things work at this web site: You show us what you've accomplished so far, and then we explain any parts of your reasoning that are not correct. If you are unable to accomplish or explain anything, then you need to design a specific question for us, and we will answer it.

As far as I can tell, you do not know the definition of the terms "maximum", "minimum", "inflection point", the concept of "slope", or the meaning of the notation f'(x).

If I am wrong, then PLEASE let me know what you know. Tell me WHY you cannot start this exercise. Once I understand your roadblock, I can help you. I'm not willing to spend much time trying to GUESS what people need.

Cheers,

~ Howard I. Noe