# Geometrical proof question

1. Dec 30, 2007

### disfused_3289

Prove that the graph of y= ax^3 + bx^2 + cx + d has two distinct turning points if
b^2> 3ac. Find values of a,b,c and d for which the graph of this form has turning points at (0.5, 1) and (1.5, -1)

2. Dec 30, 2007

hi iam a new member to this site

well here isolved first part of it
differentiate the whole equation with respeact to x

you will get

3ax^2+2bx+c

find the maxima and minima

i.e for two turning points two distinct max,min must exist

Discriminant>0

(2b)^2-12ac>0
4*b^2 > 12 ac
b^2 >3 ac...prooved

Last edited: Dec 30, 2007
3. Dec 30, 2007

second part

3ax^2+2bx+c=0 was the equation i already mentioned
multiplying them we get 3/4

2=-2b/3a
-b=3a

3/4=c/3a
4c=9a

substituting value of function in the function equation we get

a+2b+4c+8d=8
27a+18b+12c+8d=-8

solve these equations simultaniously
for a,b,c,d

we get

d=-1
a=4
b=-12
c=9

if iam correct

Last edited: Dec 30, 2007
4. Dec 30, 2007

### mathwonk

Last edited: Dec 30, 2007
5. Dec 30, 2007

I dont understand your last statement ..