MATH 1131Q Study Guide - Quiz Guide: Intermediate Value Theorem, Asymptote

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

5.2 5.3 Chase Clay ton Worksheet 12 Math 165 Fall 2017 1. Let uer) and v(x) be functions of z and consider the function u(x) | f(t) dt u(x) F(x) = where f is a continuous function (a) Find an expression forf FG) (b) Compute this expression if u(x) sinx,r(x)-x2 cos(re), and f(x)-vz2sinz 2 Assuming that f(x) dx = 2 and g(z) dz -4, evaluate/2f (x) 3g(a) dr. -30-4) 3. Assunne that / 3/(r) dz--2, / 5f(x) dr 7, and f(z)--1 and evaluate f(x) da and 3f (x) +2 dz. 4. Since f(x) S If(a) for all z show that f(x) dx If(x)ld 5. Assume that for b > 0 that f(x) dx = 1-b-1. Use this to calculate the following: (a) f(x) dz. (b) 3f(x) -4da. 6. Use geometric reasoning to justify the following "facts" (a) If /(z) is even then Lf(z)dz=rf(z)dz. (b) If f(r) is odd then ()dr o.