Review in calc I to prepare for calc II

In summary, when optimizing a function in calculus, it is important to find the critical points of the first derivative. To determine which critical point to use, you can use the first derivative test, where a negative derivative before the point indicates a maximum and a positive derivative indicates a minimum. Alternatively, you can use the second derivative test, where a negative second derivative indicates a maximum, a positive second derivative indicates a minimum, and a zero second derivative indicates a bending point. This method can be helpful in determining the nature of a critical point.
  • #1
ranger
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I'm doing a review in calc I to prepare for calc II. I'm now applications of derivatives (optimization). Okay so when I have the function I need to optimize, I need to take the derivative and find the critical point of the first derivative. But sometimes there's more than one critical point. Is there any sort of test that I can do to find which critical point I should use.

--thank you.
 
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  • #2
Why not a first derivative test? I assume you have done one before. If the derivative is negative until the critical point, then positive after the critical point then you have a maximum. The other way around for a minimum. Essentially limits with derivatives.
 
  • #3
Ah the first derivative test. Thanks for the input.
 
  • #4
Mindscrape said:
Why not a first derivative test? I assume you have done one before. If the derivative is negative until the critical point, then positive after the critical point then you have a maximum. The other way around for a minimum. Essentially limits with derivatives.

Other way around, if the derivative is negative to the critical point and the positive after the value at that point is a minimum, because the function decreases to that point and then increases.
 
  • #5
You could also get the second derivative and evaluate it in the critical points (where the first derivative is zero). If the second derivative is negative you have a maximum, if it's positive you have a minimim and if it's zero you have (what i directly translate from dutch, because I don't know what it's called in english) a bending point, as you would have in the function y=x^3. If calculating the second derivative isn't too much work, I generally use this method to establish the nature of a critical point.
 

1. What topics should I review in calc I to prepare for calc II?

To prepare for calc II, it is important to review the fundamental concepts and skills from calc I, such as limits, derivatives, and integrals. It is also helpful to review algebra and trigonometry, as they are used extensively in calc II.

2. How can I practice my calculus skills before starting calc II?

There are many resources available for practicing calculus skills, such as online practice problems, textbooks, and study guides. You can also attend review sessions or work with a tutor to practice your skills.

3. Is it necessary to have a strong foundation in calc I to do well in calc II?

While a strong foundation in calc I is helpful for success in calc II, it is not necessarily required. However, it is important to have a good understanding of the basic concepts and skills from calc I before moving on to more complex topics in calc II.

4. What are some common mistakes to avoid in calc I review for calc II?

Some common mistakes to avoid when reviewing calc I for calc II include relying too heavily on memorization instead of understanding the concepts, not practicing enough problems, and not seeking help when needed. It is important to have a solid understanding of calc I before moving on to calc II.

5. How can I best prepare for calc II if I struggled in calc I?

If you struggled in calc I, it is important to identify the areas where you need improvement and focus on those topics while reviewing. You can also seek help from a tutor or attend review sessions to strengthen your understanding of calc I concepts before starting calc II. It is also helpful to practice problems regularly to build your skills and confidence.

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