Find c such that f'(c) = 0 and determine whether f(x) has a local extremum at x = c. f(x ) = (x - 1)2 - 1 Find any local minima. Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. O A. The local minima is/are the value(5) which occur at x = (Simplify your answers. Use a comma to separate answers as needed.) O B. There are no local minima.Find c such that f'(c) = 0 and determine whether f(x) has a local extremum at x = c. f ( X ) = ex Find any local minima. Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. O A. The local minima is/are the value(s) which occur at x = (Simplify your answers. Use a comma to separate answers as needed.) O B. There are no local minima.Find c such that f'(c) = 0 and determine whether f(x) has a local extremum at x = c. f ( x )= x Find any local minima. Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. O A. The local minima is/are the value(s) which occur at x = (Simplify your answers. Use a comma to separate answers as needed.) O B. There are no local minima.Suppose f(x) = x3 + 5, new, 2]. (all Find the slope of the secant line connecting the points (x, y) = (o, 5} and (2. 13). (b) Find a number new: 1) such that f'{c) is equal to the slope of the secant line you computed in {a}, and explain why.r such a number must exist in {0, 2). {a} The slope ofthe secant line is .{Type an integer or a simplified fraction.) Suppose {00:455. xelO. 1]. [a] Find the slope of the secant line connecting the points (x: y}: [0: 1} and (1, e). {[1] Find a number can): 1) such that f'{c} is equal to the slope of the secant line you computed in {a}, and explain why such a number must exist in {0, 1}. [a] The slope oftne secant line is El {Type an exact answer in terms of s.) Suppose that rm: In x, xe[1, e]. {a} Find the slope of the secant line connecting the points (x, y): {1, 0) and (e, 1). (b) Find a number new: 9) such that f'(c) is equal to the slope of the secant line you computed in (a), and explain why.r such a number must exist in {1, e). A car moves in a straight line. At time t (measured in seconds), its position (measured in meters) is s(t) = 3 Osts9 . 90 (a) Find its average velocity between t = 0 and t = 9. (b) Find its instantaneous velocity for te(0, 9). (c) At what time is the instantaneous velocity of the car equal to its average velocity?dN $ 20 for all te[0, 6]. What can you say about N(6)? [Hint: Remember also that it is impossible for the number of organisms to become negative]. Denote the size of a population at time t by N(t), and assume that N(0) = 75 and dt Select the correct choice below and fill in the answer boxes to complete your choice. OA. N(6)