1)

Determine whether the function is continuous or discontinuous at the given x-value. Examine the three conditions in the definition of continuity. f(x) = * - 25 X =-5 X - 5 O The function is continuous at x = -5. O The function is discontinuous at x = -5.If the instantaneous rate of change of g(x) at (-1, -7) is 1/2, write the equation of the line tangent to the graph of g(x) at x = -1. (Let x be the independent variable and y be the dependent variable.)Consider the following figure. y = f(x) For each given x-value, use the figure to determine whether the function is continuous or discontinuous at that x-value. If the function is discontinuous, state which of the three conditions that define continuity is not satisfied. (Select all that apply.) (a) x = 5 Of is continuous. lim f(x) does not exist. O x-5 O f(5) does not exist. lim f(x) # f(5). x - 5 (b) x = -4 Of is continuous. lim f(x) does not exist. O x- -4' O f(-4) does not exist. lim f(x) # f(-4). O x--4'(c) x = -2 Of is continuous. C lim _f(x) does not exist. x - -2 Of(-2) does not exist. O lim f(x) # f(-2). x - -2 (d) x = 2 Of is continuous. lim f(x) does not exist. x - 2 O f(2) does not exist. O lim f(x) # f(2). x - 2Determine whether the given function is continuous. You can verify your conclusions by graphing the function with a graphing utility. x) - 2x2 1 "' The function is continuous. "' The function is not continuous. If it is not, identify where it is discontinuous. You can verify your conclusion by graphing the function with a graphing utility. (If the function is continuous, enter CONTINUOUS.) x - For the given function find the average rate of change over each specified interval. f(x) = x2+ x - 12 (a) [0, 9] (b) [-6, 10]In the figure, at each point A and B draw an approximate tangent line and then use it to answer the following questions. B 8 A y =f(x) " . . (a) Is f'(x) greater at point A or at point ? Explain. O f'(x) is greater at point A. The slope of the tangent line is positive at A. O f'(x) is greater at point A. The slope of the tangent line is negative at A. Of'(x) is greater at point B. The slope of the tangent line is positive at B. Of'(x) is greater at point B. The slope of the tangent line is negative at B. (b) Estimate f'(x) at point B. 0 3 Oo O 1 O W/ H O -3If the total revenue function for a blender is R(x) = 30x - 0.01x2 where x is the number of units sold, what is the average rate of change in revenue R(x) as x increases from 10 to 20 units? per unitFor the function f'(-1) for f(x) = 2x3 - 13x + 7, approximate f'(a) in the following ways. (Round your answers to four decimal places.) (a) Use f(a + h) - f(a) with h = 0.0001. h (b) Graph the function on a graphing calculator. Then zoom in near the point until the graph appears straight, pick two points, and find the slope of the line you see.This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the skipped part. Tutorial Exercise A point (a, b) on the graph of y = f(x) is given, as is the equation of the line tangent to the graph of f(x) at (a, b) is given. Find f'(a) and f(a). (4, -11); 7x - 2y = 50 Step 1 We are told that the point (4, -11) is a point on the graph of y = f(x), and that the equation of the line tangent to the graph at (4, -11) is given by 7x - 2y = 50. We want to find both f(4) and f'(4). To find f(4), we simply note that -11 is the y-value on the graph corresponding to the x-value of 4. Thus, f(4) = Submit Skip (you cannot come back)If the instantaneous rate of change of f(x) at (6, -5) is 7, write the equation of the line tangent to the graph of f(x) at x = 6. (Let x be the independent variable and y be the dependent variable.)