Mean Value Theorem Problem

[natHenderson]

I've just found the slope of the secant line from -4 to 3 to be -4/3, but I don't know what to do from there.

 

[pka]

View attachment 19137
I've just found the slope of the secant line from -4 to 3 to be -4/3, but I don't know what to do from there.

I dislike such question unless the coordinates are clear. Though not with this one.
My suggestion: draw a line segment from \((-4,f(-4))\) to \((3,f(3))\).
At how many places on the graph is the tangent to the graph parallel to that line segment?

 

[natHenderson]

Oh, that's actually a good idea, thanks!

 

[natHenderson]

Is it three times?

 

[pka]

Is it three times?

Well I said that I disliked the the question because of the imprecision.
I would say that at one point in each of \([-3,-2],~[-1,0].~\&~[1,3]\)

 

[Steven G]

Can you try that slope again? How did you get -4/3??

Before I agree with your 3 points can you please draw a straight line connecting the end points and then denote the three places you are referring to. Thanks.