Mathematics 133 -- Intensive Calculus for Science 1

Quiz 8

November 14, 2001

The eighth (and last!) regular quiz of the semester will be given in class on Friday, November 16. It will cover the material from sections 3.6, 4.1, and 4.3 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 natural logarithms and inverse trig functions:
  1. d/dx(ln(u)) = 1/u du/dx
  2. d/dx(arcsin(u)) = 1/sqrt(1 - u²) du/dx
  3. 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.
• First ``optimization'' problems -- determining the maximum and/or minimum values of continuous function on a closed interval.

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)
4. Trigonometric derivatives: d/dx(sin(x)) = cos(x) and d/dx(cos(x)) = -sin(x)

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

Good Review Problems

• Problems like Section 3.6/1 - 35
• Problems like Section 4.1/13 - 20 (derivatives and algebra first)
• Problems like Section 4.3/3, 4, 5