At x = 1 the function (in the graph below) is o continuous, differentiable o continuous,...
6. (10 points) The graph of a function fis given below. O O . a. For which values of x in the interval (-4,4) is f not continuous? Give the type of discontinuity Gump, infinite or removable) in each case. b. For which values of x in the interval (-4,4) is f not differentiable? c. Give the value of the following: lim f(x) it. limf(x) ill. lim 1.
3. (12) If the function below is continuous and differentiable everywhere within the interval (-3, 3), sketch the graph which satisfies the following conditions: f(-3) = 0, f(-2) = 3, f(-1) = 2, f(1) = -1, S (3) = -2 f'(-2) = 0 f'(x) > 0 on (-3,-2), f '(x) <0 on (-2, 3) f"(x) > 0 on (-1, 1), f '(x) <0 on (-3,-1) (1, 3)
3. (12) If the function below is continuous and differentiable everywhere within the interval [-3, 3), sketch the graph which satisfies the following conditions: f(-3) = 0, f(-2) = 3, f(-1) = 2, f(1) = -1, f(3) = -2 f'(-2)=0 f'(x) >0 on (-3,-2), f'(x) <0 on (-2, 3) f"(x) > 0 on (-1, 1), f '(x) <0 on (-3,-1) U(1, 3)
x2 +7x+12 1. Consider the function: f(x)= x +3 a. Is this function continuous at x = -3? b. Does this function have a limit at x = -3? dito c. Is this function differentiable at x = -3? d. Sketch a graph of the function in the space below. Be sure to include all pertinent features.
For the function f(x), determine whether or not f is continuous and/or differentiable at the following points. Also using only the given function (not a graph), determine what occurs graphically at these points. f(x) = 1, X, x² - 12, x < 0 0<x< 4 X > 4 (a) At x = 0, f(x) is ---Select--- . At this point, the graph of f(x) has ---Select--- (b) At x = 2, f(x) is ---Select--- . At this point, the graph...
6. (10 points) The graph of a function fis given below. O O a. For which values of x in the interval (-4,4) is fnot continuous? Give the type of discontinuity (jump, infinite or removable) in each case. b. For which values of x in the interval (-4,4) is f not differentiable? c. Give the value of the following: i. lim f(x) lll. lim f(x) X-2 X-2 X-2
7) [f function g is defined by g(x) = Ta'an, xa, thon g'(1) = ? (A) 1 (B) 2 (C) 3 (D)O (E) Does not exist The graph of function g is shown below. Which of the following statements about function g is true? A) Atx=b, function g is differentiable. BY Atxa, function g is continuous, but not differentiable. C) Atx=a, function g is both continuous and differentiable Function g is not differentiable at any point. E) Atx=c, function g...
5. 6 pt Determine whether the function f(x) is continuous and/or differentiable at x = 1. (x2+1 f(x) = { 12, >1 1 <1
Sketch the graph of a single function that has all of the properties listed. (a) Continuous and differentiable everywhere except at x = 2, where it has a vertical asymptote (b) Increasing everywhere it is defined (c) Concave upward on (-0,2) and (446) (d) Concave downward on (2,4) and (6,00) Choose the correct graph below. OA ов. O c. OD a 10 10 10 10 10 10 10 - 10
The graph of a function f is given below
(10 points) The graph of a function is given below. 2 a. For which values of x in the interval (-4,4) is f not continuous? Give the type of discontinuity Gump, infinite or removable) in each case. b. For which values of x in the interval (-4,4) is fnot differentiable? c. Give the value of the following: i. lim f(x) ii. lim f(x) tit. lim f(x)