1. 8.1 Exponential Functions & Differentiation
“The biggest challenge in life is being yourself… In a world trying to make you like everyone else.” CoolNSmart.com Warm – up: Graph y = 2ex. Identify each: Domain, Range, asymptote(s), intercept(s).

2. Review and Refresh
How do you determine the slope of a function at a point, using Calculus?
Describe the chain rule.

3. The derivative of y = ex The slope at (0, 1) is 1.
The slope at (1, e) is e.
m = 1
m ≈ 2.718

4. New Derivative Rules
Derivative of Natural Base Function: Let u be a differentiable function of x

5. Example 1
Find the slope of the tangent line to y = e-2x at the point (0, 1).
(0, 1)

6. Example 2
Find the derivative of each function: (a) (b) (c)

7. Example 2 Continued…
Practice with a partner: (d) (e)

8. Example 3
Use implicit differentiation to find dy/dx.

9. See if you can example….
Find the second derivative of the function:

10. Exit Pass
Write your name and find the derivative of each function: HW: 8.1 Day 1 Assignment

11. 8.1 Day 2 Curve Sketching & Optimization
WARM – UP:
Determine the second derivative of:
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12. Review of the day Answer these independently and then we will discuss:
How do you determine relative extrema?
How do you determine points of inflection, and what are they?

13. Graph me!!
Example 1
Find the extrema and the points of inflection (if any exist) of the function.

14. Try one with a partner:
Find extrema (justify), points of inflection (justify):

15. Last Example / Exit Pass?
The value V of an item t years after it is purchased is given by Find the rates of change of V with respect to t when t = 1 and t = 5.