5. Use the Second Derivative Test to find all local extrema, if the test applies. If it does not, state why and then use the First Derivative Test. f (x ) = -x4-8x3 -4 6. Consider the following function: f ( x ) = (x - 3) (x+ 6) 2 Step 1. Determine f ' (x) and f"(x). Step 2. Determine where the function is increasing and decreasing. State your answers in interval notation. Step 3. Determine where the function is concave up and concave down. State your answers in interval notation. Step 4. State the x-values of any local minima, maxima, and inflection points.7. Consider the following function: f (x) = 1x3 - 5x2 + 6x - 11 Step 1. Determine f' (x) and f"(x). Step 2. Determine where the function is increasing and decreasing. State your answers in interval notation. Cond (6) Step 3. Determine where the function is concave up and concave down. State your answers in interval notation. Step 4. State the x-values of any local minima, maxima, and inflection points.8. A medical equipment dealer has estimated that he can sell N(x) = 170 + 40 In( 3 + 1.5x ) pieces of medical equipment annually, where x (in thousands of dollars) is the amount spent on advertising. Step 1. Find the number of pieces of medical equipment sold if $6000 is spent on advertising. Round your answer to the nearest integer. Step 2. Find the rate of change in the number of pieces of medical equipment sold if $6000 is spent on advertising. Round your answer to the nearest integer. holla Wevipb falterj So 9 . Find the derivative of the given expression. f(x) = In( (19 - 19x3)3 ) Find the derivative of the given expression. 10. y = 18 + In( x2 )