Explain the difference between an absolute minimum and a local minimum. O A function f has an absolute minimum at x = c if f(c) is the smallest function value on the entire domain of f, whereas f has a local minimum at c if f(c) is the smallest function value when x is near c. O There is no difference. O A function f has an absolute minimum at x = c if f(c) is the smallest function value when x is near c, whereas f has a local minimum at c if f(c) is the smallest function value on the entire domain of f. O A function f has an absolute minimum at x = c if f(c) is the largest function value when x is near c, whereas f has a local minimum at c if f(c) is the largest function value on the entire domain of f. O A function f has an absolute minimum at x = c if f(c) is the largest function value on the entire domain of f, whereas f has a local minimum at c if f(c) is the largest function value when x is near c.Find the critical numbers of the function. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) f(x) = X3 + 9x2 21X Find the critical numbers of the function. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) L g(r)= y2_3y+3 Find the absolute maximum and absolute minimum values of f on the given interval. f(x) = 2x3 - 3x2 - 72x + 3, [-4, 5] absolute minimum absolute maximumFind the absolute minimum and absolute maximum values of f on the given interval. f(x) = (x2 - 1)3, [-1, 6] absolute minimum absolute maximumFind the absolute minimum and absolute maximum values offon the given interval. f(t) = W\" 25 :2, [115] absolute minimum absolute maximum Consider the equation below. f(x) = 2x3+ 3x2 - 180x (a) Find the interval on which f is increasing. (Enter your answer in interval notation.) Find the interval on which f is decreasing. (Enter your answer in interval notation.) (b) Find the local minimum and maximum values of f. local minimum local maximum (c) Find the inflection point. ( x, y ) = Find the interval on which fis concave up. (Enter your answer in interval notation.) Find the interval on which f is concave down. (Enter your answer in interval notation.)Consider the equation below. f(x) = 4x3 + 6x2 - 24x+ 9 (a) Find the intervals 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. ( x, y ) = Find the interval on which fis concave up. (Enter your answer using interval notation.) Find the interval on which fis concave down. (Enter your answer using interval notation.)Consider the equation below. f(x) = x4 50x2 + 8 (a) Find the interval on which 1' is increasing. (Enter your answer in interval notation.) Find the interval on which fis decreasing. (Enter your answer in interval notation.) (b) Find the local minimum and maximum values of 1". local minimum :1 local maximum :1 (c) Find the inection points. (X: Y) = ( ) (smaller x-value) (X; Y) = ( ) (larger X-value) Find the interval on which fis concave up. (Enter your answer in interval notation.) Find the interval on which fis concave down. (Enter your answer in interval notation.) Suppose f " is continuous on (-oo, co). (a) If f '(1) = 0 and f "(1) = 1, what can you say about f? O At x = 1, f has a local maximum. O At x = 1, f has a local minimum. O At x = 1, f has neither a maximum nor a minimum. More information is needed to determine if f has a maximum or minimum at x = 1. (b) If f '(4) = 0 and f "(4) = 0, what can you say about f? O At x = 4, f has a local maximum. O At x = 4, f has a local minimum. O At x = 4, f has neither a maximum nor a minimum. O More information is needed to determine if f has a maximum or minimum at x = 4.Consider the Function below. g[x)=210+8x3+x4 (a) Find the interval of increase. [Enter your answer in interval notation.) Find the interval of decrease. (Enter your answer in interval notation.) (b) Find the local minimum value(s). (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) Find the local maximum value(s). (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) (c) Find the interval where the graph is concave upward. (Enter your answer in interval notation.) Find the interval where the graph is concave downward. (Enter your answer in interval notation.) Find the inflection points. mw=( : ) (smaller X-value) ) (larger x-value} mw=(