Find the intervals on which the function is increasing, the intervals on which the function is decreasing, and all the local extrema for the function fix} = x4 x3. Upload your answer. Complete the following steps: Step 1: Find the derivative of f. Step 2: Find the critical numbers of f. These are where f'lxl = O or is undefined. Step 3: Since fis dened for all real numbers, form intervals using these critical numbers. Step 4: Set up a chart like the one below using these intervals and test the sign of fr at a test value in each interval. For each critical number use the rst-derivative test and the chart to decide if flc} is a local min, max or neither. Table for First Derivative Test to Find Local Extrema Intervals (314,\") Test Value Sign of f'(test value) fincreasing f decreasing Step 5: Find the y-coordinate of each critical number and state which points are local minimums, local maximums, or neither a local minimum of maximum. Note the points are (0,0) and BM, -O.1055l Question 2 10 pts Determine which of the following statement is correct for the function f (x) = 2x3 + 6x Note; There are no critical numbers for this function. To find where the function is increasing, select a single test value and plug it into the derivative. O The function f(x) is incresing for all reall numbers O The function is f(x) is decreasing for all reall numbers O The function f(x) is increasing in the interval from negative infintify to 1 and decreasing in the interval from 1 to infinity. O The function f(x) is decreasing in the interval from negative infintify to 1 and increasing in the interval from 1 to infinity