A projectile shot directly upward with a velocity of 192 ft/s moves according to the equation s = 192t - 16t- (in feet). Determine the maximum altitude (in ft). ft Suppose the derivative of a function fis f' (x) = (x - 7)5 (x + 6)5 (x- 4)4. On what interval(s) is f increasing? (Enter your answer using interval notation.) Find the extreme values of the following function. (If an answer does not exist, enter DNE.) y = X - 6x +9 (x, y ) =Find the extreme values of the following function. y = 2x3 + 13x2 + 8x + 1 smaller x-value (x, y) = larger x-value (x, y) =Find the y-values of all potential local extreme points (often called critical numbers or critical points) of g(v) = - y - 6 y2 - 3y + 18 Only consider real values of y. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) @ TutorialConsider the function f(x) = 2x - 9x2 - 24x + 9 on the interval [-2, 5]. What is the absolute minimum of f(x) on [-2, 5]? What is the absolute maximum of f(x) on [-2, 5]?Find the critical points of f(x) = 4 sin x + 4 cos x and determine the extreme values on |0, . (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) critical points X maximum A( x ) = minimum A( x ) =Consider the following function on the given interval. rm = 2 cos[t) + sin{2t], [0, ;] Find the derivative of the function. Find anv critical numbers of the function. (Enter vour answers as a comma-separated list. If an answer does not exist, enter DNE.) Find the absolute maximum and absolute minimum values of fon the given interval. absolute minimum value absolute maximum value