Please solve all these questions:

Consider the function Hm) = (av2Y1 (r''+1)(:~"'3')2 +% whose graph is shown below: 0.75 0.5 0.26 I 1.5 2.5 3 35 Which of the following best describes the point x=3? O The second derivative test implies it is a local minimum 0 It is a local minimum, but the second derivative test is inconclusive. O The second derivative test implies it is a local maximum 0 It is a local maximum, but the second derivative test is inconclusive. Q It is an inection point. 0 It is not a critical point. Question 1 1 pts Let f (ac) = - 4ac3 + 18x2 + 24x + 16. Fill in the blanks: f has an inflection point at x = f is concave down on the interval ( ) and concave up on the interval ( ). In each endpoint, write a number, 'infinity', or '-infinity'.(2 points) Find the critical point and the interval on which the given function is increasing or decreasing, and apply the First Derivative Test to the critical point. Let f(x) = 2 x2+3 ls f a maximum or minumum at the critical point? Local maximum v The interval on the left of the critical point is (0,150) . On this interval,f is increasing v Whilef' is positive v . The interval on the right of the critical point is . On this interval,f is decreasing v whilef' is negative v