estimate the local maxima and minima and identify the mulltiplicity of the factors
1) F(X)=(2X^2+2X-4)(X^2-6X+9)
estimate the local maxima and minima and identify the mulltiplicity of the factors
1) F(X)=(2X^2+2X-4)(X^2-6X+9)
You can start by factoring: F(X)= 2(X^2+ X- 2)(X- 3)^2= 2(X+ 2)(X-1)(X- 3)^2. You now know that F has zeros at x= -2, x= 1 and x= 3. Where there is a single zero, the sign changes and F(0)= (-4)(9)< 0. 0 is between -2 and 1 so F is positive for x< -2, negative between -2 and 1, negative again between 1 and 3 and still negative (because -3 is a double root) for x> 3. That indicates that there is a miminum between -2 and 1 and a maximum between 1 and 3. Since the problem only says "estimate", you can use the fact that maxima and minima tend to be halfway between zeros of polynomials.