MAT 1300 Study Guide - Midterm Guide: Maxima And Minima, Derivative, Saddle Point

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23 Dec 2012

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MAT 1300 Full Course Notes

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If x=c is not in the domain, then there are not critical points. If f"(x) is undefined, there is also a critical point. If local maximum at x=c, there will be a critical point at x=c. Always throw away points not in interval. Absolute extreme occurs at x=c if f > f(x) for every x. You must check if function is concave up from one side and concave down from the other. If there is an inflection point at x=c, then f (x)=0 or f (c) is undefined. Suppose f(x) has cp: there is a local max at x=c if concave down so f (x) > 0, there is a local minimum if p (x) > 0. 3 methods for validating the presence of absolute extrema: your function is a simple function like a parabola. A>0 (absolute min: use extreme value theorem. F(x) has an absolute maximum and minimum: thm not in book.

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If U and V are positive constants, find all critical points of the function. (Enter your answers as a comma-separated list.) F(t) = Ue t + Ve -t t = Find all critical points of f(x) = 20 x 2 e - 0.3x and classify them as local minima of ,maxima. x = (smaller value) This critical point is a . x = (larger value) This critical point is a . Consider f(x) = x 8 (7 - x) 9. Find f '(x) and simplify your answer. f '(x) = Find all critical points of f(x) and then use the first derivation test to determine local maxima and minima. f(x) has a at x = (smallest value) Local Maximum OR Minimum OR Neither f(x) has a at x = Local Maximum OR Minimum OR Neither f(x) has a at x = (largest value) Local Maximum OR Minimum OR Neither Find the inflection points of f(t) = t 4 + t 3 - 18t 2 +8. Give exact answer. t = (smallest value) t = (largest value) Sketch a possible of y = f(x), using the given information about derivation y' = f'(x) and y" = f"(x). Assume that the function is defined and continuous for all real x. Let f be a function f(x) > 0 for all x. Let g = 1/f. If f is increasing in an interval around x 0, what about g? g is increasing in an interval x 0. g is zero in an interval around x 0. g is decreasing in an interval around x 0. We cannot tell whether g is increasing or decreasing in an interval around x 0. g is constant in an interval around x 0. If f has a local maximum at x 1, what about g? g has a local maximum at x 1. g has both a local minimum and a local maximum at x 1. We cannot tell whether g has a local minimum or a local maximum at x 1. g has an inflection point at x 1. g has a local minimum at x 1. If f is a concave down at x 2, what about g? g is increasing at x 2. g is flat at x 2. We cannot tell whether g is concave up of concave down at x 2. g is concave down at x 2. g is concave up at x 2. You are given the graph of the second derivation function f" below. Which of the given have x-values that are inflection points of the function f? (Select all the apply.) A B C D E F G H I none of the above

MAT 1300 Study Guide - Midterm Guide: Maxima And Minima, Derivative, Saddle Point

MAT 1300 Full Course Notes

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