Finding the points!

[lovetolearn]

Use the graph at right to locate all of the following
a) label f, f', and f'' on the graph
b) inflection point(s)
c) critical value(s)
d) value(s) where f(0)=0
e) x-intercept(s) of f
f) identify the intervals in which f is concave up or concave down,
defending any conclusions using the graph only
g) identify the intervals in which f is increasing or decreasing




a) f starts at the lower left, thru X1, P2, X3, etc, f' starts on the left at P1, thru X2, etc, f'' is the other one
b) P3
c) x2 and x5
d) X1, X3, X6
e) same as d ?
f) concave down from start to infection point, P3. Concave up from P3 to the right
g) increasing from start to P2, decreasing from P2 to P6, then increasing to the right


Thanks so much for the help! I am stuck most on C, D, and E. I believe the others are correct.

 

[stapel]

You have posted answers for parts C, D, and E. In what sense are you "stuck"?

 

[Quaid]

c) critical value(s)

Critical value(s) of what? Function f only?

(From the graph, we see that the first derivative of f also has a critical value.)


More importantly, let's be clear on the difference between "critical value" versus "critical point".

It seems like your course has confused these because there is no way to determine a function value from a graph with no labeled, vertical axis.

A critical point is a number in the domain; a critical value is the function output when its input is a critical point.

From wikipedia article: "The value of the function at a critical point is a critical value."

d) value(s) where f(0)=0

The zero shown in red is a typographical error, yes?

The horizontal axis is not labeled, so we do not know the location of the origin.

I'm thinking they want the value(s) of x where f(x) = 0

f(0) is a constant

f(x) is a variable

Specifically, f(x) is function notation for the variable y.

a) f starts at the lower left, thru X1, P2, X3, etc, f' starts on the left at P1, thru X2, etc, f'' is the other one

b) P3

c) x2 and x5

d) X1, X3, X6

e) same as d ?

f) concave down from start to infection point, P3. Concave up from P3 to the right

g) increasing from start to P2, decreasing from P2 to P6, then increasing to the right

I'm also unclear where you're "stuck". From these answers, it appears that you've got the right idea, so I'm guessing that you're trying to ask somebody to check your answers.

Your answers for (a) and (b) look good.

Your answer for (c) is correct, IF they're trying to ask for the critical points of function f only.

Your answers for (d) and (e) are correct, IF they're trying to ask for locations where f(x)=0.

Your answers for (f) and (g) look good.

Cheers :cool:

 

[mmm4444bot]

Sorry the graph should be turned left once and then it would be right side up. It would not allow me to change it on here.

That is correct; our forum does not include image-editing features. You need to fix image issues before uploading the file.

If you use Windoze, then the MSPaint application will rotate images for you. (That's how I changed your uploaded file.)