Multiple Choice Question about Modulus Function

[Atheismo]

Homework Statement

Multiple choice question about a modulus function, which statement is false?
Below is the multiple choice question about a modulus function (the domain of the function is all reals):

Which one of the following is not true about the function f(x)= | 2x+4 | :

A. The graph of f is continuous everywhere
B. The graph of f ' is continuous everywhere ( f ' is the derivative of f)
C. f(x) is greater than or equal to zero for all values of x
D. f '(x) = 2 when x > 0
E. f '(x) = -2 when x < -2

End Question

Can someone please tell me the correct answer and why. Also, please explain to me what "continuous everywhere" means.

Thank you.

 

[Mark44]

Continuous everywhere means that f is continuous at each point.

Draw a graph of this function and draw a graph of its derivative. After you do that, you should be able to figure out which is the false statement.

 

[Atheismo]

Continuous everywhere means that f is continuous at each point.

Draw a graph of this function and draw a graph of its derivative. After you do that, you should be able to figure out which is the false statement.

But what does it mean by f is "continuous"? I don't know what that means.

Also, how do I find the derivative?

 

[Bohrok]

A continuous graph means you can draw it without lifting your pencil from the paper (one way to look at it).

To find the derivative, rewrite it as |2x+4| = √(2x+4)², since |x| = √(x²), and use the chain rule.

 

[Mark44]

But what does it mean by f is "continuous"? I don't know what that means.

Also, how do I find the derivative?

Your book should have a definition of this term, and probably has some examples of functions that are continuous and some that aren't.

If the problem is asking you about the derivative, it's reasonable for us to assume that differentiation has already been covered in your course.

 

[Atheismo]

Your book should have a definition of this term, and probably has some examples of functions that are continuous and some that aren't.

If the problem is asking you about the derivative, it's reasonable for us to assume that differentiation has already been covered in your course.

Yes it has but a while ago. I need to do some revision. I got the answer, I think, it's B right?

Answers D and E give it away lol.

 

[Mark44]

Yes, b is the one that is not true.