1. The problem statement, all variables and given/known data Find the intervals of increase/decrease. Use first derivative test to find the local maxima and minima. Sketch a rough graph. 2. Relevant equations a) f(x) = 2x2+12x-1 b) f(x) = 1/2x4-2x2 c) f(x) = 3x-4 sqrt 2 d) f(x) = x2-1/x2+1 3. The attempt at a solution A) it becomes f '(x) = 4x+12 solve for zero 4x+12=0 4x=-12 x=-3 plug x=-3 into the equation to get y value, which is 0 so... (-3, 0) is the first and only critical point. After testing it, i've determined that f(x) decreases when xE (-infinity, -3) f(x) increases when xE (-3, infinity) This is correct I believe, but I wouldn't be surprised if it's not. B) I end up with critical points (0,0) and (sqrt2, -2) My attempt is: f(x) = 1/2x4-2x2 f '(x) = 2x3-4x solve for zero 2x3-4x ------is this next step right? 2x(x2-2) = 0 2x=0 x=0 and.... x2-2=0 x2=2 x=sqrt2 (1.4142...) feels wrong already so after plugging 0 and sqrt2 into original equation give me (0,0) and (sqrt2, -2) Intervals in the end area negative, another negative, and a positive value. C) the derivative of this would be 3, which leaves no x value to determine. D) quotient rule to find derivative, which I think is 4x/(x2+1)2 I think I need a math tutor, this course is killing me.