which means that f ′ ( x + h ) < 0 {\displaystyle f'(x+h)<0} if h < 0 (intuitively, f is decreasing as it approaches x from the left), and that f ′ ( x + h ) > 0 {\displaystyle f'(x+h)>0} if h > 0 (intuitively, f is increasing as we go right from x). Now, by the first derivative test, f {\displaystyle f} has a local minimum at x {\displaystyle x} .