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posted by  jtstur2 on 11/23/2008 1:20:32 PM  |  status: Live  

proof (lifesaver)

Course Textbook Chapter Problem
Calculus N/A N/A N/A
Question Details:
find f if f "(x) = 2x-3 and f '(0) = 12 and f(0) = 6
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Apprentice
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posted by benpharmer on 11/23/2008 1:29:49 PM  |  status: Live
Asker's Rating: Helpful   
Response Details:
f'(x)=x^2-3x+c
0^2+3(0)+c=12
f'(x)=x^2-3x+12

f(x)=(1/3)x^3-(3/2)x^2+12x+c
(1/3)0^3-(3/2)0^2+12(0)+c=6
f(x)=(1/3)x^3-(3/2)x^2+12x+6
Oracle
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posted by Altair on 11/23/2008 1:33:58 PM  |  status: Live
Asker's Rating: Lifesaver   
jtstur2's comment:
"thanks much"
Response Details:
let
 
 
=>
 
 
compare both sides we have:
 
2(2-1)a2 = -3 => a2 =-3/2
3(3-1)a3 = 2 => a3 = 1/3
 
a4 = a5 =...an=0 for all n>4
 
the solution is:
 
 
y(0) = 6 => a0 = 6
y'(x) = a1 - 3x + x2
y'(0) = a1 = 12
 
the final solution is:
 
 
 
 
 
 
 

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