Video narration
Is every point where f'(x)=0 automatically a maximum or minimum? Picture a road. At a hilltop, you climb toward the top, then descend. That is a local maximum: nearby, the function rises and then falls. In a valley, you descend first, then climb out. That is a local minimum. But here is the turn: being flat is only a candidate. f'(x)=0 alone does not prove a maximum or minimum. Test both sides of the point. If f' is positive before it and negative after it, it changes from rising to falling: maximum. If f' changes from negative to positive, falling to rising: minimum. If the sign does not change, the flat point is neither. So, is every flat point an extreme? No. f'(x)=0 केवल candidate है; sign change proves it-positive to negative, maximum; negative to positive, minimum. यही rule याद रखें with ZENITH ACADEMY KHATIMA.