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#1 2010-02-10 04:50:58
- Avva
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derivative and average rate of change
If , rate of change of this function =-3/4 at x=4 , and the average rate of change =-5/6 when x changes from 4 to 3.8 ,
FIND the values of a and b.
THNX in advance
Last edited by Avva (2010-02-10 04:51:52)
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#2 2010-02-10 15:15:25
- bobbym
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Re: derivative and average rate of change
Hi Avva;
A question. I usually see f(x) = a / (x + b), when I see F(x) that usually means F(x) = ∫ f(x) dx = a / (x + b). What do you think?
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#3 2010-02-11 09:29:18
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Re: derivative and average rate of change
Actually I didn't study it that way am in high school so we learn only headlines Thnx 4 ur help
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#4 2010-02-11 15:45:37
- bobbym
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Re: derivative and average rate of change
Hi Avva;
Okay, just wanted to know whether I should differentiate once or twice. I'll chance one because it is easier.
The instantaneous rate of change of a function is the derivative. So:
Now the rate of change of this function = -3 / 4 at x = 4: So substituting x = 4
In order to uniquely determine the parameters a and b we need 2 equations to solve simultaneously. I gave you one, can you get the second one? Hint, use the average rate of change.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#5 2010-02-11 17:22:19
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Re: derivative and average rate of change
sorry for bothering you I just wanna know which solution is right MANYYYY Thnx
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#6 2010-02-11 18:34:31
- bobbym
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Re: derivative and average rate of change
Hi Avva
Are the 2 equations. The roots are a = 3 and b = -2.
b = -4 does not work. Can you tell me why?
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#7 2010-02-11 20:25:26
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Re: derivative and average rate of change
when I substitute with -4 in rate of change and average rate of change it didn't give me the given values
but with -2 it did Is this the right reason???
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#8 2010-02-11 20:38:17
- bobbym
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Re: derivative and average rate of change
Hi Avva;
Yes, but look at what happens when you substitute b = -4 in either equation. You get zero in the denominator. Division by zero is undefined so you can stop right there.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#9 2010-02-11 21:07:34
- Avva
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Re: derivative and average rate of change
many thnx highly appreciated 
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#10 2010-02-11 21:09:01
- bobbym
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- Registered: 2009-04-12
- Posts: 109,606
Re: derivative and average rate of change
Hi Avva;
Glad to help.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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