Mathematics 133 -- Intensive Calculus for Science 1

Quiz 8

November 8, 2005

The eighth regular quiz of the semester will be given in class on Friday, November 11. It will cover the material from sections 3.5, 3.6, and 4.1 from this week's problem set. You may use a calculator on this quiz. The specific topics to be covered will be:

• Additional ``shortcut rules'' for computing derivatives of functions involving trig functions, natural logarithms, and inverse trig functions:
  1. d/dx(sin(x)) = cos(x) and d/dx(cos(x)) = -sin(x)
  2. d/dx(ln(u)) = 1/u du/dx
  3. d/dx(arcsin(u)) = 1/sqrt(1 - u²) du/dx
  4. d/dx(arctan(u)) = 1/(1 + u²) du/dx
• Critical points, local maxima and minima, and the first and second derivative tests for classifying critical points.

You will need to be able to use the derivative rules above in conjunction with our other shortcut rules:

1. The product rule: d/dx(f(x)g(x)) = f(x)g'(x) + g(x)f'(x)
2. The quotient rule: d/dx(f(x)/g(x)) = (g(x)f'(x) - f(x)g'(x))/(g(x))²
3. The chain rule: d/dx(f(g(x)) = f'(g(x)) g'(x)

On the quiz, there will be two or three questions similar to problems from the assignment.

Good Review Problems

• Problems like Chapter 3 Review/1 - 66 (you should be able to find the derivative of all these now)
• Problems like Section 4.1/13 - 20 (derivatives and algebra first)