# Mean Value Theorem Problem

#### natHenderson

##### New member

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

##### Elite Member
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

##### New member
Oh, that's actually a good idea, thanks!

#### natHenderson

##### New member
Is it three times?

#### pka

##### Elite Member
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 $$[-3,-2],~[-1,0].~\&~[1,3]$$

#### Jomo

##### Elite Member
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.