Find the critical points and the intervals on which the function f (x) = 6x2 7x 13 is increasing or decreasing. Use the First Derivative Test to determine whether the critical point is a local minimum or maximum (or neither). Find the x-coordinates of the critical points that correspond to a local minimum. (Use symbolic notation and fractions where needed. Give your answer in the form of a comma separated list. Enter DN E if there are no critical points.) Find the x-coordinates of the critical points that correspond to a local maximum. (Use symbolic notation and fractions where needed. Give your answer in the form of a comma separated list. Enter DN E if there are no critical points.) Find the intervals over which the function is increasing and decreasing. (Use symbolic notation and fractions where needed. Give your answers as intervals in the form (ate, at). Use the symbol 00 for innity, U for combining intervals, and an appropriate type of parenthesis "(",")", "[","]" depending on whether the interval is open or closed. Enter El if interval is empty.) the function is increasing on the function is decreasing on Find the critical points. y(x) = x(x - 13)? (Use symbolic notation and fractions where needed. Give you answer as a comma-separated list.) C= Determine if the function is increasing or decreasing on the interval (Cmin, (max) . increasing O decreasing Use the First Derivative Test to determine whether the critical point max yields a local min or max (or neither). O Maximum Neither O MinimumFor the given function, nd the critical points (3 and the intervals on which the function is increasing or decreasing. g(x) = 6x5 + 6x3 + 6x In addition, determine which critical points identify a local minimum and which critical points identify a local maximum. If no points or intervals exist for a particular value, enter DNE. c= li decreasing intervals= \\ mm\" = \\\\ Find the critical point(s) of the function. f(x) = x2 - 9x'1 (Give your answer in the form of a comma-separated list of values. Express numbers in exact form. Use symbolic notation and fractions where needed. Enter DNE if the function has no critical points.) critical point(s}: For each critical point, identify if it is the location of a local minimum or a local maximum. (Give your answer in the form of a comma-separated list. Express numbers in exact form. Use symbolic notation and fractions where needed. Enter DNE if the function has no local minimum or local maximum.) local minima at x = local maxima at x = Find the intervals on which f is increasing or decreasing. (Give your answer as an interval in the form (at, in). Use the symbol on for innity. U for combining intervals. and an appropriate type of parenthesis "\Consider the function 2x+ xJ=x2+a Find the critical point(s) of f. (Give your answer in the form of a comma-separated list. Express numbers in exact form. Use symbolic notation and fractions where needed. Enter DNE if the function has no critical points.) critical point(s}: Use the First Derivative Test to determine whether the critical point(s} yield(s) a local minimum or a local maximum. (Give your answer in the form of a comma-separated list. Express numbers in exact form. Use symbolic notation and fractions where needed. Enter DNE if the function has no local minimum or local maximum.) local minima at x = local maxima at x = Find the intervals on which the function is increasing or decreasing. (Give your answer as an interval in the form (\"2\"). Use the symbol on for innity. U for combining intervals. and an appropriate type of parenthesis "(","J", "\"[,\"\"] depending on whether the interval is open or closed. Enter E! if the interval is empty. Express numbers in exact form. Use symbolic notation and fractions where needed.) f is increasing on f is decreasing on Find the critical point[s) of the function y = 9 2 cos {9} at 9 E [21. 4x]. (Give your answer in the form of a comma-separated list of values. Express numbers in exact form. Use symbolic notation and fractions where needed. Enter DNE if the function has no critical points.) critical point(s}: Determine the x-coordinates of the critical point(s) that correspond(s} to a local minimum or a local maximum. (Give your answer in the form of a comma-separated list. Express numbers in exact form. Use symbolic notation and fractions where needed. Enter DNE if the function has no local minimum or local maximum.) local minima: local maxima: Find the intervals on which the function is increasing or decreasing. (Give your answer as an interval in the form (at, 1:). Use the symbol on for innity. U for combining intervals, and an appropriate type of parenthesis "(".")\" "\"[.\"\"] depending on whether the interval is open or closed. Enter El if the interval is empty. Express numbers in exact form. Use symbolic notation and fractions where needed.) increasing: decreasing: Two days after he bought a speedometer for his bicycle, Lance brought it back to the Yellow Jersey Bike Shop. "There is a problem with this speedometer," Lance complained to the clerk. "Yesterday I cycled the 22-mile Rogadzo Road Trail in 71 minutes, and not once did the speedometer read above 15 miles per hour!" "Yeah?" responded the clerk. "What's the problem?" To explain Lance's complaint, first compute his average velocity. (Use decimal notation. Give your answer to two decimal places.) average velocity: miles/hour How did Lance use the Mean Value Theorem to explain his complaint? There is at least one moment of time when Lance's speed is equal to his average speed. At that moment Lance's speed exceeds the speed of 15 miles/hour. O For 50% of time, Lance's speed exceeds his average speed that in turn is above 15 miles/hour. O As Lance's average speed is greater than 15 miles/hour, at any moment of time the speedometer should show the speed that is above 15 miles/hour