Post #4

After three days of school last week, I felt as if those days were spent on reviewing what we have already covered, First Derivative Test and Second Derivative Test. The steps should already be ingrained in people's heads but if not here are the steps:

First Derivative Test:
1. Take the derivative of the original problem.
2. Set the first derivative equal to Zero.
3. Solve for x.
4. Create intervals for x. i.e. (-∞, 1) (1, 4) (4, ∞)
5. Pick a number in the intervals then plug that number in the first derivative for x.
6. Solve. For positive numbers, the graph of the derivative is above the x-axis. For negative numbers, the graph of the derivative is below the x-axis. The numbers for x are your points of inflection. (Points of Inflection are only if there is a shift in the graph!!!)

Second Derivative Test:
1. Take the derivative of the first derivative.
2. Set the second derivative equal to Zero.
3. Solve for x.
4. Create intervals for x. i.e. (-∞, 1) (1, 4) (4, ∞)
5. Pick a number in the intervals then plug that number in the second derivative for x.
6. Solve. For positive numbers, the graph of the derivative is above the x-axis. For negative numbers, the graph of the derivative is below the x-axis. The numbers for x are your points of inflection. (Points of Inflection are only if there is a shift in the graph!!!)

One thing I am still having troubles grasping is the chain rule. Say you have (x+1)^(2). I see the problem as x^n, so I bring the 2 out in front then subtract the exponent by 1 leaving me with 2(x+1)^(1). It does not make sense to me that you have to multiply by the derivative of the inside also because the rule does not call for it. Can someone please explain why you have to take the derivative of the inside also?