Slope at x=0

[smile4me8d21]

I am not sure why I am not getting this right. Find the slope of the graph of ƒ at x = 0, showing all work. ƒ(x) = x³ - 4x + 2. I believe I am trying then to find the slope at the point (0,2). The derivitve is 3x^2-4. At x=0 is the slope 4? If someone could please let me know what I am doing wrong here with a detailed answer?
Aditionally I need to know when an object is in motion with this function. the points which it is at rest, moving in a positive direction and a negative direction. i thought I was correct in: is moving in a negative direction from (-infinity,-2/√3), at rest at2/√3, and moving in a positive direction from (2/√3,infinity).

 

[Deleted member 4993]

I am not sure why I am not getting this right. Find the slope of the graph of ƒ at x = 0, showing all work. ƒ(x) = x³ - 4x + 2.

I believe I am trying then to find the slope at the point (0,2). Correct

The derivitve is 3x^2-4. At x=0 is the slope 4? No. It is -4

If someone could please let me know what I am doing wrong here with a detailed answer?
Aditionally I need to know when an object is in motion with this function. the points which it is at rest, moving in a positive direction and a negative direction. i thought I was correct in: is moving in a negative direction from (-infinity,-2/√3), at rest at2/√3, and moving in a positive direction from (2/√3,infinity).

I am not sure about the second part of your question. To find speed - it must be a function of time.

 

[HallsofIvy]

I am not sure why I am not getting this right. Find the slope of the graph of ƒ at x = 0, showing all work. ƒ(x) = x³ - 4x + 2. I believe I am trying then to find the slope at the point (0,2). The derivitve is 3x^2-4. At x=0 is the slope 4? If someone could please let me know what I am doing wrong here with a detailed answer?
Aditionally I need to know when an object is in motion with this function. the points which it is at rest, moving in a positive direction and a negative direction. i thought I was correct in: is moving in a negative direction from (-infinity,-2/√3), at rest at2/√3, and moving in a positive direction from (2/√3,infinity).

Assuming that x= time, the velocity is given by the derivative \(\displaystyle 3x^2- 4= (\sqrt{3}x- 2)(\sqrt{3}x+ 2)\). If \(\displaystyle x< -2/\sqrt{3}\) then both factors are negative so their product is positive and the object is moving in the positive direction. If \(\displaystyle x> 2/\sqrt{3}\) then both factors are positive so their product is positive and the object is moving in the positive direction. What happens if \(\displaystyle -2/\sqrt{3}< x< 2/\sqrt{3}\).