Derivative f'(x) and Information that can be extrapolated from it

[takmok11]

For this graph, y=f'(x)



Q1. At x=1 f(x) has a...

Answer Choices:

local maximum
point of inflection
local minimum
point of nondifferentiability
point of discontinuity

I'm not sure how to answer this one. If the graph above was f(x), then I know at x=1, you can't take the derivative. However, I am not sure when the graph is f'(x)

Q2. Over the interval (-4,4), how many local maxima does f(x) have.

I drew a number line for this. I labeled all the points at which f'(x)=0. I then found x=0 is the only local extrema because the sign changes from + to -. Is this correct?

 

[Deleted member 4993]

For this graph, y=f'(x)



Q1. At x=1 f(x) has a...

Answer Choices:

local maximum
point of inflection
local minimum
point of nondifferentiability
point of discontinuity

I'm not sure how to answer this one. If the graph above was f(x), then I know at x=1, you can't take the derivative. However, I am not sure when the graph is f'(x)

Q2. Over the interval (-4,4), how many local maxima does f(x) have.

I drew a number line for this. I labeled all the points at which f'(x)=0. I then found x=0 is the only local extrema because the sign changes from + to -. Is this correct?

What is the definition of "point of non-differentiability " - according to your class-notes or textbook?

For f(x) to have local extrema - what should be the value of f'(x)? (I do not understand your statement - "because the sign [of f'(x)]changes from + to - .")

 

[Dr.Peterson]

Q1. At x=1 f(x) has a...

Answer Choices:

local maximum
point of inflection
local minimum
point of nondifferentiability
point of discontinuity

I'm not sure how to answer this one. If the graph above was f(x), then I know at x=1, you can't take the derivative. However, I am not sure when the graph is f'(x)

The fact that the graph of f' turns sharply means that f' can't be differentiated there; so f'' doesn't exist. That isn't one of the choices.

What is the definition of a point of inflection?

Q2. Over the interval (-4,4), how many local maxima does f(x) have.

I drew a number line for this. I labeled all the points at which f'(x)=0. I then found x=0 is the only local extrema because the sign changes from + to -. Is this correct?

Yes. That is the only place where f' is zero and changes from positive to negative, so it is the only local maximum