With a test Monday, I'm kind of scared. I understand the First Derivative Test and Second Derivative Test, but most of the vocabulary is screwing me up. Some words are simple and commonly seen, while others are rare to find, so some do not recognize them as well as others.
These are the terms that I know so far:
1. Points of Inflection-relates to the Second Derivative Test
2. Extrema, Critical numbers, and intercepts- relates to the original graph (found using the First Derivative Test)
3. Intervals-relates to both the First Derivative Test and Second Derivative Test (depends on which intervals need to be found)
4. f'-first derivative
5. f"-second derivative
There is one question on 3.3 Homework Quiz that really throws me off. It is: "A differentiable function f has a critical number at x=2 and no other critical numbers. f'(1)=(-3) and f'(3)=5. Identify the relative extrema of f at x=2." I'm just utterly confused with what to do. I do know that differentiable means a derivative, probably the first derivative, but after that I'm lost. Can anyone help me with this problem?
A little reminder if people still can't remember both tests:
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.
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.
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"A differentiable function f has a critical number at x=2 and no other critical numbers. f'(1)=(-3) and f'(3)=5. Identify the relative extrema of f at x=2."
ReplyDeleteokay so to do this..you look at what it give you...first we know that two is a critical number but that's all we now and we have to find the extreama of it. In order to do this look at the rest of the question. It says: f'(1)=(-3) and f'(3)=5
so looking at the first one you know that it's negative...so it's gonna go down first [like decreasing or concave up would do] then looking at the second one you know that it's positive...so it's gonna go up first [like increasing or concave down would do]
so if it goes from decreasing to increasing we know that it looks like a 'U'
well...we know that x=2 is in the middle of this which is gonna be at the tip of the 'U', making x=2 a MIN!
THAT'S YOUR ANSWER!..i think