1a find all points xy where the derivative is 0 2a Find the

1a. find all points (x,y) where the derivative is 0

2a. Find the x values where the derivative is 0

2b. Find any points of inflection

1) f(x) = -2x^2 - 12x +1

derivative : f\'(x) = -4x -12

f\'(x) =0 ; -4x -12 =0

x = -3

y = f(-3) = -2(9) - 12(-3) +1 = -18 + 36 +1 = 19

(x, y) = ( -3, 19)

2) f(x) = x^3 + 3x^2 - 9x +1

f\'(x) = 3x^2 + 6x -9

f\'(x) =0 ; 3x^2 + 6x -9 =0

x^2 + 2x -3 =0 ; x^2 + 3x -x -3 =0

(x+3)(x-1) =0

x= -3 ; x =1

Inflection point: f\"(x) = 6x + 6

f\"(x) =0 ; x= -1

f(-1) = 12

Point ( -1 , 12)