- #1
Marcus27
- 11
- 1
Homework Statement
I understand how to solve for stationary points, and then take the second derivative and input the values of x to determine the nature of the stationary points, if x > 0 then the stationary point is a minimum and if x < 0 then the stationary point is a maximum. What I am having difficulty with is the concept.
Homework Equations
If f(x) = x^3 -3x^2 + 4
f'(x) = 3x^2 -6x
f''(x) = 6x - 6
Lets say that f(x) gives the distance traveled by a car after x seconds, so f'(x) would give a speed graph, and f''(x) would be an acceleration graph. However, solving for the stationary point of the graph f(x)
f'(x) = 0
3x^2 -6x = 0
3x(x-2) = 0
Stationary points are (0,4) and (2,0)
Plugging these values into the acceleration function,
f''(0)= 6(0) - 6 = -6
f''(2) = 6(2) -6 = 6
This is all well and good but I do not understand how a car can be traveling at 0 speed and have a negative or positive acceleration.