If fis an invertible function, which of the following is not true? O If fis 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 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
The graph of a function fis given. Use the graph to estimate the following. (Enter your answers using interval notation.) (a) The domain and range of f. domain range (b) The intervals on which fis increasing and on which fis decreasing. increasing decreasing
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.
Suppose that f(x) is a continuous function over all real numbers, f'(- 10) = 0, and f''( - 10) = 24 Which of the following is true? (Hint: 2nd derivative test) Which of the following is true? (Hint: 2nd derivative test) O A. f(x) has a relative minimum at x = - 10 W O B. f(x) is decreasing when x = - 10 O C. f(x) is increasing when x = - 10 O D. f(x) has a relative...
ha (predict the tuto por certain town 5. A function fis said to be continuous at x = a if f(a) is defined, if lim f(x) exists, and if lim/(x) = f(a). Use this definition to explain why the following function is not continuous at x = 2. Include in your explanation an accurate sketch of this function. Also be sure to state specific values of "a", lim f(x), and f(a) in your response. Slx - 21 if x #...
is: 6. (8 points) / is a function that is continuous on (-0,00). The first derivative of /"(x) = (3x - 1)x+3X5 - x) Use this information to answer the following questions about : a. On what intervals is increasing or decreasing? Internal in which fis increasing or -- 8x-1) (x+3)(5-x) > 0 x=112, -3, -5 b. At what values of x does f have any local maximum or minimum values? - V2 ; Location(s) of Minima: Location(s) of Maxima:...
Graph of A continuous function fis defined on the closed interval - 4sxs6. The graph of consists of a line segment and a curve that is tangent to the x-axis at x-3, as shown in the figure above. On th interval Dexc6, the function fis twice differentiable, with f(x)>0. Is there a value of a -4sach, for which the Mean Value Theorem applied to the interval (a 6), guarantees a value ca cx6, at which f'(c) = ? Justify your...
2. Find the intervals on which the following function is continuous. tan r B( ) = V4-12 3. Find the derivatives of the following functions (a) f(z)= /5x +1 (b) gla) = (2r -3)(a2 +2) (c) y = In (x + Vx2 - 1) 4. Find the intervals on which the following function is decreasing. f(z) = 36x +3r2 - 2r 5. Evaluate the following integrals. r dr (a) sec2 tan (b) dar 3 (c) da 5x+1 1. Sketch the...
Given f(x) = 2x - 3x - 36x +6. (a) Find the intervals on which fis increasing or decreasing. (b) Find the relative maxima and relative minima of f. Select one: a. (a) Increasing on (-3,2), decreasing on (-0, -3) and (2,00) (b) Rel. max. f(2)= 62 rel. min. f(-3) = -33 o b. None of these c. (a) Increasing on (-2, 3), decreasing on (-00,-2) and (3,0) (b) Rel. max. f(3) = 75, rel. min. f(-2) = -50 d....
need help with these.please. I-8 Let f(2) Find the open intervals on which fis increasing (decreasing). Then determine the x-coordinates of +8 all relative maxima (minima). 1. f is increasing on the intervals 2. fis decreasing on the intervals 3. The relative maxima of f occur at - 4. The relative minima off occur at 2 - Notes: In the first two your answer should either be a single interval, such as (0,1), a comma separated list of intervals, such...