2. [0/2 Points] DETAILS PREVIOUS ANSWERS LARCALCET7 4.R.015. MY NOTES Determine whether the Mean Value Theorem can be applied to f on the closed interval [a, b]. (Select all that apply.) f(x) = 14 - x1, [1, 5] Yes, the Mean Value Theorem can be applied. O No, because f is not continuous on the closed interval [a, b]. No, because f is not differentiable in the open interval (a, b). O None of the above. X If the Mean Value Theorem can be applied, find all values of c in the open interval (a, b) such that f'(c) = f(b) - f(a). b - a (Enter your answers as a comma-separated list. If the Mean Value Theorem cannot be applied, enter NA.) c = -1 X 3. [0/1 Points] DETAILS PREVIOUS ANSWERS LARCALCET7 4.R.095. MY NOTES A rancher has 400 feet of fencing with which to enclose two adjacent rectangular corrals (see figure). What dimensions should be used so that the enclosed area will be a maximum? ( x, y ) = 200 ft 3 X4. [1/2 Points] DETAILS PREVIOUS ANSWERS LARCALCET7 4.R.009. MY NOTES Determine whether Rolle's Theorem can be applied to f on the closed interval [a, b]. (Select all that apply.) f(x) = x3 - 27x - 6, [-3, 6] Yes, Rolle's Theorem can be applied. No, because f is not continuous on the closed interval [a, b]. O No, because f is not differentiable in the open interval (a, b). O No, because f(a) * f(b). If Rolle's Theorem can be applied, find all values of c in the open interval (a, b) such that f'(c) = 0. If Rolle's Theorem cannot be applied, explain why not. (Enter your answers as a comma-separated list. If Rolle's Theorem cannot be applied, enter NA.) C = -3.6 X6. [1/5 Points] DETAILS PREVIOUS ANSWERS LARCALCET7 4.R.033. MY NOTES Consider the following function. f (x ) = X + 5 x 2 (a) Find the critical numbers of f, if any. (Enter your answers as a comma-separated list. ) X = -10 (b) Find the open intervals on which the function is increasing or decreasing. (Enter your answers using interval notation. If an answer does not exist, enter DNE.) increasing (-10,00) X decreasing (-00, - 10) X (c) Apply the First Derivative Test to identify all relative extrema. (If an answer does not exist, enter DNE.) relative minimum ( x, y ) = DNE X 4 relative maximum ( x, y ) = 20 X8. [1/4 Points] DETAILS PREVIOUS ANSWERS LARCALCET7 4.R.040. MY NOTES The function s(t) describes the motion of a particle along a line. s(t) = 6:3 32: + 8 (a) Find the velocity function v(t) of the particle at any time t 2 0. vm = 1&2 32 'J (b) Identify the time interval(s) on which the particle is moving in a positive direction. (Enter your answer using interval notation.) (0.0.253),(2._ \"25) DO X (c) Identify the time interval(s) on which the particle is moving in a negative direction. (Enter your answer using interval notation.) (d) Identify the time(s) at which the particle changes direction. (Enter your answers as a comma-separated list.) r = 025321725 X