Second derivative test for local extrema: if a is a critical point and the second derivative f ¨(a) is
positive, i.e. f ¨(a) > 0, then a is a local minimum point. If f ¨(a) is negative, i.e. f ¨(a) < 0, then a
is a local maximum point. For f(x) the derivative is equal to f'(x)=4x+2 and the second derivative is equal to f''(x)=4 this value is a positive value which indicates a local minimum point. If we equal the derivative to zero, f'(x)=4x+2=0 the x value would be equal to -1/2. The answer is E.