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posted by  chibba on 1/23/2008 12:11:44 AM  |  status: Live  

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Course Textbook Chapter Problem
Calculus N/A N/A N/A
Question Details:
Determine the coefficients a, b, c, d so that the curve whose equation is y = ax3 + bx2 + cx + d has a maximum at (-1, 10) and an inflection point at (1, -6).
Do not use L'Hopital's Rule on my post unless it's neccessary!
 
Feel free to msg me if you have any questions with my responses!
 
The indeterminate forms include 00, 0/0, 1∞, ∞ - ∞, ∞/∞, 0×∞, and ∞0.

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posted by Yashar Bahman on 1/23/2008 12:44:25 AM  |  status: Live
Asker's Rating: Helpful   
chibba's comment:
"the answer is not right but ty for ur help"
Response Details:

since the inflection pt is at 1, -6 that means
f double prime of   1 must equal 0  and that f(1) must equal -6

so find f double prime
f prime = 3ax2+2bx+c
f doubleprime = 6ax+2b 

f " (1) = (3a+b)  = 0
3a = -b

since there's a max at -1 then f prime must equal 0 and f (-1 ) must equal 10
so f prime = 3ax2+2bx+c
f ' (-1) = 0 = 3a - 2b - c
we know 3a = -b
-b -2b -c = 0
-3b = c

f(1) = -6 = ax^3+bx^2+cx+d = a + b + c + d = -b/3+b-3b+d
so -7/3b+d = -6 or d = 7/3b - 6

f(-1) = 10 = ax^3+bx^2+cx+d = -a+b-c+d = b/3+b+3b+7/3b-6 = 20/3b-6 = 10

20/3b-6 = 10
6.66b=16
b= 2.4

then plug it in to the other ones
-3b = c
-3(2.4) = c = -7.2

-b/3 = a
-2.4/3 = a = -0.8

d = 7/3b - 6
7/3(2.4)-6 = d =  -0.4

FINALLY
a = -0.8
b =  2.4
c =  -7.2
d =  -0.4
Tags: Math, Calculus
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