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## Homework Statement

The slope of the curve y = ax(cubed) + bx(squared) + c is -12 at its point of inflection (2,-11), find a,b,c.

## Homework Equations

f ' (x) = 3ax(squared) + 2bx

f " (x) = 3ax + 2b

## The Attempt at a Solution

f ' (x) = 3ax(squared) + 2bx

-12 = 3a2(squared) + 2b(2)

-12 = 12a + 4b

b = -3a - 3

-12 = 3a(2)(sqrd) + 2(-3a -3)

a = -1

b = 0

-11 = ax(cubed) + bx(sqrd) + c

c = -3