Give the RMIN and RMAX for the function f(x)=x+16x  . Give both the x and y value as an ordered pair. If none exist, list “none” for both x and y.  RMIN=([BLANK-1], [BLANK-2])  and RMAX= ([BLANK-3], [BLANK-4])

Match each function to it’s point of inflection. If the graph has no point of inflection, select “none”. 

Find the location and value of all relative extrema for the function.  

Determine all intervals on which the function is increasing.  y=2×3-12×2+18x+3 (Choose all that apply)

Find the points of any relative extrema for f(x) = x3 – 3×2 + 1

Identify the location(s) of the Absolute Maximum for the given graph.

Decide if the given value of x is a critical number for f, and if so, decide whether the point for x on f is a relative minimum, relative maximum, or neither. f(x) = (x2 – 6)(2x – 3); x = 1/2

S(x) = -x3 + 6×2 + 288x + 4000, 4 ≤ x ≤ 20 is an approximation to the number of salmon swimming upstream to spawn, where x represents the water temperature in degrees Celsius. Find the temperature that produces the maximum number of salmon.

Answer Format: Do not enter $ sign nor decimals. Each answer will be a whole number. An office supply company sells x mechanical pencils per year at $p per pencil. The price equation for these pencils is p=10 – 0.001x. Determine the revenue function (R=xp) and use it along with its derivative to find: a) how many pencils must be sold in order to maximize revenue. x=[BLANK-1] b) the maximum revenue. R = $ [BLANK-2] c) the price (p) that yields maximum revenue. p = $ [BLANK-3] Furthermore, suppose cost is C(x)=5000 + 2x. Use this and the above information to answer the following. d) how many pencils must be sold to maximize profit (P=R-C)? x=[BLANK-4] e) find the maximum profit. P = $ [BLANK-5]  

Use derivatives to answer the following about:  f(x)=x2x2+7 a) The points ±213, 14  are [BLANK-1] b) The points ±212, 14  are [BLANK-2] c) The point (0,0) is a(n) [BLANK-3]. d) The function does not have a [BLANK-4].