Home A to Z Index Contact Us
You are here: Citrus College > Academics > Courses > Anderson Printable version Print this page

Intro to Calculus

  1. Let    f(x) = xmath + 2x - 3   and   g(x) = 3x + 7. Find the following: (12 points)

    1. f(-5)
    2. g(2a)
    3. f(b+1)
    4. g[f(x)]

  2. Let f times x = x squared + x minus 12 over x squared + 2x minus 15 Notice that when x =1, f(x) = 0/0 which is undefined.

    1. Draw the graph of this function by plotting points. (5 points)
    2. Use the graph to find the limit of  f(x) as xmath symbols1. (5 points)

  3. math symbol Use factoring to find the limit of f(x) as xarrow3. (8 points)

  4. We already know the linear function f(x) = 3x - 4 has slope 3 and y-intercept -4.

    1. Find two points that rest on this line. Show, using these points with the slope formula, that the slope is 3. (6 points)
    2. Let a and b each represent a real number. Then (a, f(a)) and (b, f(b)) represent points that rest on this line. Now show, using these points with the slope formula, that the slope is 3. (6 points)

  5. The graph of the quadratic function f(x) = xmath symbol squared is a parabola. Since this is a curve instead of a straight line, its slope is not a constant number.

    1. Approximate the slope of f(x) = xmath symbol squared at the point (1,1) by finding the slope of the line passing through (1,1) and (2,4). Then, improve your approximation by finding the slope of the line passing through (1,1) and (1.0001, 1.00020001). (6 points)
    2. What do you think is the slope of f(x) = xmath symbol squared at the point (1,1)? (4 points)

  6. Even though the slope of f(x) = xmath symbol squared is constantly changing, it can be represented by a function called the derivative.

    1. Find the derivative of f(x) = xmath symbolsquared by finding the slope of the line passing through the points (x, f(x)) and (x + h, f(x + h)) and taking the limit of this as harrow0. (6 points)
    2. Find the derivative of f(x) = 4xsquared + 5x - 7. (12 points)
    3. Find the derivative of f(x) = xsquared. (12 points)

  7. The distance in feet covered by a car moving along a straight road x seconds after starting from rest is given by the function f(x) = 2xsquared + 48x.

    Find the velocity of the car after:

    1. x seconds (8 points)
    2. 3 seconds (5 points)
    3. 10 seconds (5 points)
    (Hint: Take the derivative of the given distance function. This will give you the velocity function.)
BONUS QUESTION: Maximizing Volume
A box with an open top is to be constructed from a square piece of cardboard, 3 feet wide, by cutting out a square from each of the four corners and bending up the sides. Find the largest volume that such a box can have. (15 points)
 
SearchGo Search
Mail this page
Citrus College 1000 West Foothill Boulevard Glendora, CA 91741-1899 (626) 963-0323

Web site developed by SectorPoint, Inc.