Loading in 5 sec....

CHAPTER 5 SECTION 5.4 EXPONENTIAL FUNCTIONS: DIFFERENTIATION AND INTEGRATIONPowerPoint Presentation

CHAPTER 5 SECTION 5.4 EXPONENTIAL FUNCTIONS: DIFFERENTIATION AND INTEGRATION

- By
**ryder** - Follow User

- 113 Views
- Uploaded on

Download Presentation
## PowerPoint Slideshow about 'CHAPTER 5 SECTION 5.4 EXPONENTIAL FUNCTIONS: DIFFERENTIATION AND INTEGRATION' - ryder

**An Image/Link below is provided (as is) to download presentation**

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript

### CHAPTER 5SECTION 5.4EXPONENTIAL FUNCTIONS:DIFFERENTIATION AND INTEGRATION

This means…

and…

Exponential and log functions are interchangeable.

Start with the base.

Change of Base Theorem

Solve.

We can’t take a log of -1.

- Example 3: Find dy/dx:

- Example 3 (concluded):

- THEOREM 2
- or
- The derivative of e to some power is the product of e
- to that power and the derivative of the power.

- Example 4: Differentiate each of the following with
- respect to x:

- Example 4 (concluded):

Theorem:

1. Find the slope of the line tangent to f (x) at x= 3.

Theorem:

1. Find the slope of the line tangent to f (x) at x= 3.

- Example 7: Graph with x≥ 0. Analyze the graph using calculus.
- First, we find some values, plot the points, and sketch
- the graph.

- Example 4 (continued):
- a) Derivatives. Since
- b) Critical values. Since the derivative
for all real numbers x. Thus, the

- derivative exists for all real numbers, and the equation
- h(x) = 0 has no solution. There are no critical values.

- Example 4 (continued):
- c) Increasing. Since the derivative for all real numbers x, we know that h is increasing over the entire real number line.
- d) Inflection Points.Since we know that the equation h(x) = 0 has no solution. Thus there are no points of inflection.

- Example 4 (concluded):
- e) Concavity. Since for all real numbers x, h’ is decreasing and the graph is concave down over the entire real number line.

Download Presentation

Connecting to Server..