1. Find all the critical numbers of the function (Justify Your Answer) (a) [5Vx – 2 f(x) = x > 2 2.x2 +3x - 14 x< 2 (Hint: Also investigate the existence of the derivative at x=2) (b) f (x) = x² – 2 ln x

Let f(x) = 2x³ – x² – 3 1. Find the first derivative of the function. (This function can be easily factored without using the quadratic formula). 6x²-x=0 X (6x-1) X=0) 6x-1= x=1 6x=1 6 2. Where are the relative extrema, if they exist? Show all parts of the analysis necessary to determine these point(s). Label everything you do. f'(x) = 6x²-x 3. Find the second derivative of the function. (This function can be easily factored without using the quadratic formula). 4. Find the inflection point(s), if there are any. Show all parts of the analysis necessary to determine these point(s).

Find the second derivative of x³ - 5x² + x = 0. A. 10x-5 B. 6x-10 C. 3x + 10 D. 3x² - 5x Given the function f(x) = x to the 3rd power -6x+2. Find the first derivative at x = 2. A. 6 B. 7 C. 3x²-5 D. 8