Math

1.) Answer the following questions for the function f(x) = (2x+4)^4

a) Determine all relative extrema of f(x)



b) Determine the intervals on which f(x) is concave upward or concave downward



c) Find the absolute extrema of f(x) on [-3,2]




2.) Determine the intervals on which f(x) = (x-1)^1/3 is increasing or decreasing.




3.) Determine the absolute extrema of f(x) = x^2/(x^2+1) on [-1,1]




4.) Determine the relative extrema of f(x) = 3x-36x^1/3




5.) Determine all intervals on which f(x) = x^3 - 3/2x^2 - 12x is concave upward or concave downward, and also find all points of inflection.





6.) Evaluate the following limits

a) lim 5x^5+x-4/2x^5+14x
x->infinite


b) lim 5x^3 + 1/6x^4-1 
x->infinite


c) lim 5x^2 +1/5x-1
x-> infinite


For #6 where it says infinite its the infinite symbol


7.) Determine all vertical asymptotes of f(x) = x^2+6x-7/x^2-49




8.) If a revenue function is given by R(x)= 30x^2/3 - 2x, find the number of units x that produce a maximum revenue.




9.) A farmer plans to fence a rectangular pasture adjacent to a river. No fencing is needed along the river. The pasture must contain 180,000 sq meters of land. What dimensions must the pasture be in order to use the least amount of fencing?