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 Post subject: AP Calculus AB Summer Homework Help
PostPosted: Tue Aug 09, 2011 1:17 pm 
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I have AP Calculus AB summer work, and I'm having trouble working out some of the problems. I'll probably be posting a few others as well. Any help would be appreciated!

x 0 1 2 3 4 5 6
f(x) -10 -8 -1 0 5 7 2

Using the table of values given above, find the average of change for f on the interval (2,5) and write an equation for the secant line passing through the corresponding points.

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 Post subject: Re: AP Calculus AB Summer Homework Help
PostPosted: Tue Aug 09, 2011 1:20 pm 
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Average of change for f on the interval (2,5) = df/dx = [7-(-1)]/(5-2) = 8/3

That's then the gradient of your line, m=8/3.

Then just solve for y=mx+c (derive c) based on the two points, y=7 when x=5, and y=-1 when x=2.

gives c= y-mx = 7-8/3*5 = ... (based on the first point)

Or, c = y-mx = -1-8/3*2 = ... (based on the second point)

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Last edited by KelvinS on Tue Aug 09, 2011 1:31 pm, edited 1 time in total.

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 Post subject: Re: AP Calculus AB Summer Homework Help
PostPosted: Tue Aug 09, 2011 1:31 pm 
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Kelvin Stott wrote:
Average of change for f on the interval (2,5) = df/dx = [7-(-1)]/(5-2) = 8/3

Thanks for the quick reply, but can you explain what you did there?

Thanks!

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 Post subject: Re: AP Calculus AB Summer Homework Help
PostPosted: Tue Aug 09, 2011 1:33 pm 
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portal1920 wrote:
Kelvin Stott wrote:
Average of change for f on the interval (2,5) = df/dx = [7-(-1)]/(5-2) = 8/3

Thanks for the quick reply, but can you explain what you did there?

Thanks!

Yep, you're basically just calculating the gradient between the two points where x=2 (f=-1) and x=5 (f=7), so you can ignore all the other points/data.

I've also added some hints on the next part, above. :D

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 Post subject: Re: AP Calculus AB Summer Homework Help
PostPosted: Tue Aug 09, 2011 2:18 pm 
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Kelvin Stott wrote:
Then just solve for y=mx+c (derive c) based on the two points, y=7 when x=5, and y=-1 when x=2.

gives c= y-mx = 7-8/3*5 = ... (based on the first point)

Or, c = y-mx = -1-8/3*2 = ... (based on the second point)

So, would the line be y=(8/3)x+(19/3)?

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 Post subject: Re: AP Calculus AB Summer Homework Help
PostPosted: Tue Aug 09, 2011 2:49 pm 
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Just came across another one.

Given that h(x) = (tan^-1)[1-(pi)(x)] is a composite function of the form h(x)=f(g(x)), find f and g.
[I think may be referring to the previous problem where f(x)=x/(x-1), and g(x)=1/(x-1), but I have no idea.]

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 Post subject: Re: AP Calculus AB Summer Homework Help
PostPosted: Tue Aug 09, 2011 2:51 pm 
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portal1920 wrote:
Kelvin Stott wrote:
Then just solve for y=mx+c (derive c) based on the two points, y=7 when x=5, and y=-1 when x=2.

gives c= y-mx = 7-8/3*5 = ... (based on the first point)

Or, c = y-mx = -1-8/3*2 = ... (based on the second point)

So, would the line be y=(8/3)x+(19/3)?

Just put x=2 and then x=5 back into your equation to make sure the line runs through those two points. Sorry for not giving you a direct answer, but you should do some of the thinking for yourself. :wink:

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