Mathematics 133 – Intensive Calculus for Science 1 Things to Know – Quiz 4 October 4, 2000

The fourth graded quiz of the semester will be given in class on Friday, October 6. There will be three or four questions similar to problems from the fourth problem set. You should know the following material.

1) Derivative at a point f′(a):

a) Know how to estimate f′(a) from a graph of y = f(x), given scales on x and y axes and relate that to properties of f such as whether f is increasing or decreasing at x = a

b) Know how to compute f′(a) from the limit definition

f′(a) = lim_{h→0} \frac{f(a + h) − f(a)}{h}

for “simple” functions f(x) like linear or quadratic polynomials.

c) Know how to estimate f′(a) numerically by finding \frac{f(a+h)−f(a)}{h} for h tending to 0.

2) Derivative functions:

a) Know how to sketch an approximate graph of y = f′(x) given a graph of y = f(x). If I ask a question like this, I would most likely give just a “qualitative” graph of y = f(x) (i.e. only showing where the original function is increasing, decreasing, where the turning points (if any) are, but not detailed information like exact scales on the coordinate axes)

b) Know how to compute f′(x) from the limit definition

f′(x) = lim_{h→0} \frac{f(x + h) − f(x)}{h}

for “simple” functions f(x) like linear or quadratic polynomials.

Good Review Problems:

1) Section 2.2/problems 3, 12, 13, 14, 23

2) Section 1.10/problems like 13, 24, 25, 26, 27,