Question

Find the correct values for the equation -x^3 +bx^2 +cx + d, using this information, local min x= -5, local max (1,11). Point of inflection = -2.

Answer 1

I assume you mean
y or f(x) = -x^3 +bx^2 +cx + d
if so
y' = -3 x^2 + 2 b x + c
and
y" = -6 x +2 b

at x = -5 , y' = 0
-75 -10 b + c = 0

at x = 1 , y' = 0
-3 + 2 b + c = 0
so
2 b + c = 3
-10 b + c = 75
-----------------subtract
12 b = -72
b = -6
then
-12 + c = 3
c = -15
put in y = 11 at x = 1 to get d
11 = -1 -6 -15 + d
d = 33

Answer 2

Hmmm. I get

y = -x^3+bx^2+cx+d
y' = -3x^2+2bx+c
y" = -6x+2b

inflection at x = -2 means
-6x+2b = 0
b = -6
y = -x^3 - 6x^2 + cx + d

extrema at x = -5,1
y' = (x+5)(x-1)
= x^2+4x-5
we need -3x^2, so
y' = -3x^2-12x+15
so c = 15
y = -x^3 - 6x^2 + 15x + d

f(2) = 11, so
11 = -1-6+15+d
d = 3
y = -x^3 - 6x^2 + 15x + 3

Answer 3

then
-12 + c = 3
c = -15 No, +15 !!!!
put in y = 11 at x = 1 to get d
11 = -1 -6 -15 + d
d = 33