Loading in 5 sec....

2014 AP CALCULUS AB FRQsPowerPoint Presentation

2014 AP CALCULUS AB FRQs

- By
**torie** - Follow User

- 97 Views
- Uploaded on

Download Presentation
## PowerPoint Slideshow about ' 2014 AP CALCULUS AB FRQs' - torie

**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

Average rate of change = lbs/day

On the fifteenth day the amount of grass clippings is decreasing at the rate of 0.1635 lbs/day

Average amount of clippings: decreasing at the rate of 0.1635

Solvedays

Tangent line at decreasing at the rate of 0.1635 is

Solve days

y decreasing at the rate of 0.1635 = 4

f(x)

y decreasing at the rate of 0.1635 = 4

f(x)

y decreasing at the rate of 0.1635 = 4

f(x)

, therefore if decreasing at the rate of 0.1635 g(x) increases . This happens on the intervals and (−3, 2)

If g(x) i decreases. This happens on and (0, 4)

g(x)is increasing and concave down on and (0, 2)

The slope of the graph of decreasing at the rate of 0.1635 f at is −2, so

Average acceleration of train A: decreasing at the rate of 0.1635

S meters/minute2

Since decreasing at the rate of 0.1635 is differentiable, it is also continuous so the Intermediate Value Theorem applies to for . Therefore, there must be at least a value such that meters/minute

meters decreasing at the rate of 0.1635

Train B decreasing at the rate of 0.1635

meters

meters

meters

z = distance between the two trains

y

Train A

x

At minutes,

f decreasing at the rate of 0.1635 has a local minimum when its derivative, f’, switches from negative to positive. This occurs at x = 1.

f decreasing at the rate of 0.1635 is twice differentiable so its derivative, f’, is both continuous and differentiable. Therefore the Mean Value Theorem can be used on f’ .

There must be a value for such that

Since

The problem can also be done using Rolle’s Theorem: decreasing at the rate of 0.1635 f is twice differentiable so its derivative, f’, is both continuous and differentiable.

And since Rolle’s Theorem can be used on f’.

Therefore, there must be a value for such that

Equation of the tangent line: decreasing at the rate of 0.1635

Using (0, decreasing at the rate of 0.1635 1):

Download Presentation

Connecting to Server..