19.) complete (a) and (b)

19x) Consider the following y=1/2x²-x (find a,b,c,d,e)

19y) Find the derivative of the function y= 5e^4x²

20. 21. Complete (a) and (b). You can verify your conclusions by graphing the functions with a graphing calculator. (3) Use analytic methods to evaluate the limit. (If the limit is innite, enter 'eo' (b) What does the result from part (a) tell you about horizontal asymptotes? The result does not yield any information regarding horizontal asymptotes. The result indicates that there are no horizontal asymptotes. The result indicates that there is a horizontal asymptote. D ETAI I: Consider the fol lowing. -1 2- y2x x (3) Find y' = f'(x). f'(x) = (b) Find the critical value. x: (c) Find the critical point. (ny) =( ) (d) Find intervals of x-values where the function is increasing. (Enter your answer using interval notation.) (e) Classify the critical point as a relative maximum, a relative minimum, or a horizontal point of inflection. In each case, check your conclusions with a graphing utility. (If an answer does not exist, enter DNE.) relative maxima relative mi ma horizontal point of inflection (x. y) =( (x.y)=(l:) (x.y)=(l: Find intervals of x-values where the function is decreasing. (Enter your answer using interval notation.) ) ) D ETAI l5 Find the derivative of the function. y = 5&4X2 or '-eo', as appropriate. If the limit does not othenuise exist, enter DNE.)