\fFor the function shown below, find (if the quantity exists) (A) I'm f(x), (B) I'm f(x), (C) lim f(x), and (D) f(0). x -+ 0+ X- 0- x-0' f ( x ) = 8-x2, for xso 8 + x2, for x> 0Determine whether f is differentiable at x = 0 by considering lim T(0 + h) - f(0) h - 0 h f(x) = 16 - x| Choose the correct answer below. O A. The function f is differentiable at x = 0 because the graph has a sharp corner at x = 0. O B. The function f is differentiable at x = 0 because both the left- and right-hand limits of the difference quotient exist at x = 0. O C. The function f is not differentiable at x = 0 because the left- and right-hand limits of the difference quotient do not exist at x = 0. D. The function f is not differentiable at x = 0 because the left- and right-hand limits of the difference quotient exist at x = 0, but are not equal.Given f(x) = x2 - 4x, (A) Find f'(x), (B) Find the slopes of the lines tangent to the graph offat x = - 2, O, and 3 (0) Graph f, and sketch in the tangent lines at x: - 2, 0, and 3. (A) W) = l: (B) The slope of the tangent line at x= 2 is El. The slope of the tangent line at x = 0 is D. The slope of the tangent line at x = 3 is D. (C) Graph f, and sketch in the tangent lines at x: - 2, 0, and 3. Click to enlarge \\ graph DEED] \"EYE \"1\"" 51V Q q mi a: Annual limousine production for the selected years is given in the table below. (A) Letx represent time (in years) since 1980, and let y Limousines represent the corresponding production of Year Produced limousines. Enter the data in a graphing calculator 1980 2300 and find a cubic regression equation for the data. __ . , . 1985 6400 (B) Let L(x) denote the regression equation found In part (A) with coefficients rounded to the nearest 1990 3900 hundredth Find L(12) and L'(12). 1995 3000 (C) Interpret L(17) and L'(17) in this context. 2000 5200 (A) L(x) = |:| (Use integers or decimals rounded to the nearest hundredth for any numbers in the equation.) (B) L(12)e |:| L112): E] (Type an integer or decimal rounded to the nearest hundred as needed.) (C) Interpret L(17) z 3200 in the context of the problem. i A. The number oflimousines produced in 1997 was 3200. i B. In 1997 the number of limousines produced was increasing by 3200 per year. i ' C. The number oflimousines produced 17 years from now will be 3200. Interpret L'(17) z; 500 in the context of the problem. In 1997 the number of limousines produced was increasing by 500 per year. A i . B. There will be 500 more limousines 17 years from now. C The number oflimousines produced in 1997 was 500. D The number oflimousines produced 17 years from now will be 500