It is known that the image of the function f (x) = x ^ 3 + ax ^ 2 + BX is tangent to the line 9x-y + 8 = 0 (- 1, - 1) (1) Find the analytical formula of F (x) (2) Find the extreme value of F (x)

It is known that the image of the function f (x) = x ^ 3 + ax ^ 2 + BX is tangent to the line 9x-y + 8 = 0 (- 1, - 1) (1) Find the analytical formula of F (x) (2) Find the extreme value of F (x)

Tangent point on function
So - 1 = - 1 + a-b
a-b=0,a=b
f(x)=x^3+ax^2+ax
f'(x)=3x^2+2ax+a
F '(- 1) = 3-2a + a = 3-A, that is, the tangent slope at (- 1, - 1) is 3-a
Tangent 9x-y + 8 = 0 slope is 9
So 3-A = 9
a=-6
f(x)=x^3-6x^2-6x
f'(x)=3x^2-12x-6=0
x=2±√6
X2 + √ 6, f '(x) > 0, increase
2-√6

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