What you should know before taking Math 231 (calculus 2)

Students planning to enroll in  Math 231 should be familiar with the following concepts covered in calculus 1:

Examples:   
•  Limits such as:
 ,    

• Derivatives and general rules for taking derivatives.
• Definition of the derivative and it's geometrical interpretation.
• Using the derivative to find local minimum and maximum for a given function.
• Using the derivative to find a good representative plot of a function.
• Derivatives of well-known functions like , Ln[x], Sin[x], Cos[x], and polynomials.
• Chain rule and product rule for taking derivatives.
• Intervals where a function is increasing or decreasing.
• What does the sign of the second derivative tell you about the behavior of a function?

Examples:
1) Find derivatives of the following functions:
    a) f(x)=
    b) f(x)=Cos()
    c) f(x) = 2Ln()
    d) f(x)=(4+12x)
    e) f(x)=
    f) f(x)=
    g) f(x)=
    h) f(x)=
2) Find the maximum and minumum of the function f(x)=-6on the interval [-1, 3].
3) Without looking at the function plot, decide whether the function f(x)=-3x has a local maximum or local minimum at x = 1 ?
(Hint: use second derivative)
4) Plot a function f(x)=(-1) (your plot should show function's max/min, where it is increasing/decreasing and the global behavior).
5) Sketch the derivative of the following function:

* Definition of the integral, it's basic properties and geometric interpretation.
• Definite vs. Indefinite integral
• Recognize and be able to use the Fundamental Theorem of Calculus. If
            f[x]=g[t]dt ,
then
            [x]=g[x].

Examples:
1) Calculate the following integrals:
    a) dx
    b) (3-x)dx
    c) 1dx
    d) dx
    e) dx

2) Calculate the area enclosed by the function plots of f(t)=t  and f(t)= .

Created by Mathematica  (May 21, 2007)