Consider the equation below. (If an answer does not exist, enter DNE.) f(x) = x5 In(x) (a) Find the interval on which f is increasing. (Enter your answer using interval notation.) Find the interval on which f is decreasing. (Enter your answer using interval notation.) (b) Find the local minimum and maximum values of f. local minimum value local maximum value (c) Find the inflection point. (х, у) %3D Find the interval on which f is concave up. (Enter your answer using interval notation.) Find the interval on which f is concave down. (Enter your answer using interval notation.)

Consider the function below. B(x) = 3x2/3 - x (a) Find the interval of increase. (Enter your answer using interval notation. If an answer does not exist, enter DNE.) Find the interval of decrease. (Enter your answer using interval notation. If an answer does not exist, enter DNE.) (b) Find the local maximum value(s). (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) Find the local minimum value(s). (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) (c) Find the inflection point. (If an answer does not exist, enter DNE.) (х, у) %3D Find the interval where the graph is concave upward. (Enter your answer using interval notation. If an answer does not exist, enter DNE.) Find the interval where the graph is concave downward. (Enter your answer using interval notation. If an answer does not exist, enter DNE.)

Physical Science: Height of a Thrown Object. A rock is thrown directly upward with an initial velocity of 50 ft/sec from an initial height of 10 ft.The velocity of this rock is modeled by the function v(t)= -32t +50, where t is in seconds, v is in feet per second, and t=0 represents the moment the rock is released. a) Determine a distance function has a function of t(in this case, "distance" is the same as"height".Be sure to consider the fact that at t=0,the rock is 10ft above the ground. b)Determine the height and the velocity of the rock after 3 sec.

Consider the equation below. In x f(x) %D 5Vx (a) Find the interval on which f is increasing. (Enter your answer using interval notation.) Find the interval on which f is decreasing. (Enter your answer using interval notation.) (b) Find the local maximum value of f. (c) Find the inflection point. -(C (х, у) %3 Find the interval on which f is concave up. (Enter your answer using interval notation.) Find the interval on which f is concave down. (Enter your answer using interval notation.)