following properties. . f (z) is decreasing at z- 5 - f (2) has a local minimum at a . f (7 ) has a local maximum at 7 - Using this information I can come to the conclusion that f'(-2) - 0 and f'(2) - 0 which means that both are factors of f'(x) This means that f'(x) can be f'(x) = =(x + 2)(x-2) and everything will come out to O when plugged in for x(-5, -2. 2) From here, I can simplify -(x+2)(x-2) by using the foil method then combining like terms together -(x + 2) (x - 2) (x + 2 (x - 2) Multiply the negative x(x - 2) - 2(1 - 2) Distributive property a (b + c) = -to-2*-2- 2(x 2) Distributive property -172 - 2*-2- 2x - 2*-2 Distributive property -12 +2x - 2x + 4 Combine like terms - x'+4 Simplify by subtracting 2x and 2x Now I have f'(x) --x^2+4 and I can se dy/dx to find my function dy = - x2 +4 dy = (-x2 +4) dx J dy = f-x2 + 4dx set up integral y + C1 - f - x2 + Ada Use constant rule y + Ci - - fx'dx + f Adx Split to multiple integrals a y + C1 = -(323 + C2) + fAdx Power rule on z y + Ci = - (323 + C2) + 4x + C3 Constant rule y= -323 + 4x Simplify Now I'm left with f(x) - -(1/3)x^3+4x for my function