7 Calculus Questions

1.

Use the graph to state the absolute and local maximum and minimum values of the function. (Assume each point lies on the gridlines. Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) y = f(x) X absolute maximum value X absolute minimum value X local maximum value(s) X local minimum value(s) XFind the absolute maximum and absolute minimum values of f on the given interval. f(t) = tv 64 - t2, [-1, 8] absolute minimum value X absolute maximum value 32The graph of the first derivative f' of a function f is shown. (Assume the function is defined only for 0 s x s 9.) YA (a) On what interval(s) is f increasing? (Enter your answer using interval notation.) (b) At what value(s) of x does f have a local maximum? (Enter your answers as a comma-separated list.) X = At what value(s) of x does f have a local minimum? (Enter your answers as a comma-separated list.) X = (c) On what interval(s) is f concave upward? (Enter your answer using interval notation.) On what interval(s) is f concave downward? (Enter your answer using interval notation.) (d) What are the x-coordinate(s) of the inflection point of f? (Enter your answers as a comma-separated list.) X =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 f is 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) = 3 cosz(x) 6 sin(x), o s x s 2:: (a) Find the interval on which 1' is increasing. (Enter your answer in interval notation.) E 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 maximum \\ (c) Find the inflection points. mn=d (x, y) = (I ' ) (larger x-value) Find the interval on which f is concave up. (Enter your answer in interval notation.) Find the interval on which 1' is concave down. (Enter your answer in interval notation.) E ) (smaller x-value) Consider the equation below. f(x) = e3" + 6" (a) Find the intervals on which 1' is increasing. (Enter your answer using interval notation.) E Find the interval on which 1' is decreasing. (Enter your answer using interval notation.) H (b) Find the local minimum value of f. U (c) Find the interval on which f is concave up. (Enter your answer using interval notation.) U (a) Find the critical numbers of the function fix) = x5(x 2J5. = (smallest value) = (largest value) (b) What does the Second Derivative Test tell you about the behavior of fat these critical numbers? At x = , the function has ---Select--- . (c) What does the First Derivative Test tell y0u? (Enter your answers from smallest to largest x value.) At x = , the function has ---Select--- . At x = , the function has ---Select-- 3 . At x = , the function h V ---Se|ect--- a local minimum a local maximum Submit Answer neither a minimum nor a maximum