CALCULUS I Second Semester

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CHAPTER 3

3.1 - 3.3

In this section we learned the different types of functions and how they can be turned into derivatives. We learn about derivatives of exponential functions and learn abou the product and quotient rule .

3.4 - 3.10

after learning about finding derivatives of simple functions, we begin to look at the different rules that are needed to be followed in order to find more complex derivatives. We learn about the chain rule, quotient rule, combining exponential functions, as well as trigonometric functions.

Combining these chapters we are able to solve problems involving related rates. We are able to calculate the rate and time at which a certain volume container might take to be filled or reach a certain volume after said time.

3.11

Here we learn specifically about hyperbolic functions and the new set of rules that are needed to be followed in order to calculate the derivatives of these functions. This chapter seems to use the ideas from previous chapters but is not used very much later on.

CHAPTER 4

4.1 - 4.7

Here we learn about finding the minimum and maximum values of functions and how this relates to first and second derivatives of functions. We learn about concavity and how to find inflection points and how these all relate to eachother.

Learning this helps with graphing out the functions and how to visualize where a line is curved towards and minimum and maximum values. We are also able to use derivatives and its curves and inflection points in order to find the optimum value of a function. This can be helpful in business and managing production and sales.

4.9

We are then introduced to Anti-derivatives. We take second derivatives and work backwards to find the first derivative and original function. We also learn about the importance of constants within anti-derivatives as well as how to find those.

The anti-derivative is a very useful tool and will be used repeatedly throughout the rest of the course.

CHAPTER 5

5.5

Finally, we learn about substitution method. This is a very important way of solving complex anti-derivatives. We substitute in variables such as "U' or "V" and work backwards from there.

5.4

We then start to learn about definite and indefinite integrals. We use derivatives and anti derivatives to find the area under the curve at within a certain boundary.

5.1 - 5.3

Here, we begin to use much more complex problems involving all that we have learned up to this point. this includes, derivatives, anti-derivatives, trigonometric functions, and all the different rules needed to follow along with that.

From this we specifically get into finding the area under a curve using right and left endpoints as well as midpoints.