Math 131 Take Home Quiz 4 Print Name________________________________

Section or class time_____________________

In problems 1 and 2, you compare the graphs of two functions which look very similar. the first one is a constant times the standard normal bell curve, as discussed in class.

1. (The standard normal curve is f(x).)

Show all you are asked to find.

a) Find and .

b) Find f '(x), make a sign chart and find the x and y coordinates of the maximum of f.

c) Find f "(x), make a sign chart and find both inflection points.

2.

a) Find and .

b) Find g'(x) , make a sign chart and find the x and y values of the max point.

c) Find g"(x) , make a sign chart and find both inflection points.

d) Graph f of problem 1 and g in the same graph using the window Xmin=-10, Xmax=10 Ymin=0, Ymax=1 Sketch the picture and show which is f and which is g.

3. Find each derivative.

Use log rules first!

4. The inflection point of a logistic function.

a) Find and .

b) Solve for x in terms of y and express it as a difference of natural logs.

c) Find .

d) Find and find the y value of the inflection point.