If the function f (x) = (x ^ 3) + ax ^ 2 + BX + A ^ 2 has an extreme value of 10 when x = 1, what are the values of A.B?

If the function f (x) = (x ^ 3) + ax ^ 2 + BX + A ^ 2 has an extreme value of 10 when x = 1, what are the values of A.B?

The derivation is as follows
3x ^ 2 + 2aX + B = 0, where x = 1
Simultaneous equation 1 + A + B + A ^ 2 = 10
The solution is a = 4, B = - 11
Or a = - 3, B = - 3

The value of the algebraic formula ax & sup3; - 10x square + 6x + C / 3x & sup3; + BX square - 2x + 4 is a constant. Find the value of a, B, C and the algebraic formula

Let ax ^ 3-10x ^ 2 + 6x + C / 3x ^ 3 + BX ^ 2-2x + 4 = K
ax^3-10x^2+6x+c=3kx^3+bkx^2-2kx+4k
(a-3k)x^3-(10+bk)x^2+(6+2k)x+(c-4k)=0
No matter what the value of X is, it always holds
So a-3k = 10 + BK = 6 + 2K = c-4k = 0
So k = - 3
So a = - 9
b=10/3
c=-12

When x = - 2, the value of ax ^ 3 + BX + 8 is 28, then when x = 2, the value of the algebraic formula ax ^ 3 + 3x ^ 2 + BX + 1

When x = - 2, the value of ax ^ 3 + BX + 8 is 28
∴-8a-2b+8=28
8a+2b=-20
When x = 2,
ax^3+3X^2+bx+1
=8a+3×4+2b+1
=(8a+2b)+13
=-20+13
=-7