Find the critical points of the following function. Use the Second Derivative Test to determine (if possible) whether each critical point corresponds to a local maximum, local minimum, or saddle point. If the Second Derivative Test is inconclusive, determine the behavior of the function at the critical points. f(x.y) = /x² +y? + 4x+5

The graph of function f(x) is shown below. At which value of is the derivative of the function equal to 2? Select the correct answer below: O z = -1 Ox=0 O x = 1 O x = 2 x=3 O -3 -2 -1 1 2 3 5 ¥ -1 -4 -5 N w 6

Follow the 5 Steps for Curve Sketching to sketch the graph of the function. r3 f (x) = - x²-3x 3 Step 1: Find the critical points and plot them on the graph on the next page. Find the first derivative. a. b. Set the first derivative equal to 0 and find where the first derivative does not exist. c. Plug the x-value of each critical point into the original function to find the y-value of the point itself. Step 2: Use the table below to test the regions to see where the function increases or decreases. Include your work for determining the sign of each interval. Intervals Sign of f'(x) Behavior of f(x) (Steps continued on the next page) Step 3: Find the possible inflection points and plot them on the graph below. a. Find the second derivative. b. Set the second derivative equal to 0 and find where the second derivative does not exist. c. Plug the x-value of each possible point of inflection into the original function to find the y-value of the point itself. Step 4: Use the table below to…

Determine all critical points for the function. y = 3x2 - 96x Select one: A.x = 0, x = 4, and x = -4 O B.x = 0 O C.x = 4 O D.x = 0 and x = 4