1. Ms. Battaglia AP Calculus

2. The inverse function of the natural logarithmic function f(x)=lnx is called the natural exponential function and is denoted by f -1 (x) = e x That is, y = e x if and only if x = lny Inverse Relationship ln(e x ) = x and e lnx = x

3. Solve 7 = e x+1

4. Solve ln(2x – 3) = 5

5. Let a and b be any real numbers. 1. 2.

6. 1. The domain of f(x)=e x is (-∞, ∞), and the range is (0, ∞) 1. The function f(x)=e x is continuous, and one-to-one on its entire domain. 2. The graph of f(x)=e x is concave upward on its entire domain. 3. and

7. Let u be a differentiable function of x. 1. 2.

8. a.b.

9. Find the relative extrema of f(x)=xe x.

10. Show that the standard normal probability density function has points of inflection when x=1, -1

11. The numbers y of shares traded (in millions) on the NY Stock Exchange from 1990 through 2005 can be modeled by where t represents the year, with t=0 corresponding to 1990. At what rate was the number of shares traded changing in 2000?

12. Let u be a differentiable function of x. 1.2.

13. Find

15. a.b.

16. a. b. c.

17.  AB: Read 5.4 Page 358 #3, 4, 11-14, 37, 38, 39-57 odd  BC: HW: Read 5.4 Page 358 #1-11 odd, 39- 59 odd,63,69,79,99, 103,105,111,121,125