. These are points where the graph reaches a local maximum (a point higher than the points on either side), or local minimum (lower than the points on either side). The tangent line always has a slope of 0 at these points (a horizontal line), but a zero slope alone does not guarantee an extreme point. Here's how to find them:  Take the first derivative of the function to get f'(x), the equation for the tangent's slope. Solve for f'(x) = 0 to find possible extreme points. Take the second derivative to get f''(x), the equation that tells you how quickly the tangent's slope is changing. For each possible extreme point, plug the x-coordinate a into f''(x). If f''(a) is positive, there is a local minimum at a. If f''(a) is negative, there is a local maximum. If f''(a) is 0, there is an inflection point, not an extreme point. If there is a maximum or minimum at a, find f(a) to get the y-coordinate. The "normal" to a curve at a particular point passes through that point, but has a slope perpendicular to a tangent. To find the equation for the normal, take advantage of the fact that (slope of tangent)(slope of normal) = -1, when they both pass through the same point on the graph. In other words:  Find f'(x), the slope of the tangent line. If the point is at x = a, find f'(a) to find the slope of the tangent at that point. Calculate −1f′(a){\displaystyle {\frac {-1}{f'(a)}}} to find the slope of the normal. Write the normal equation in slope-point form.
أوجد قيم النقاط المتطرفة على الرسم البياني أوجد معادلة عمود السطح.