Q1

(b) a relative minimum (-1; 2) (1' 5) (4, 1) -"'- None of these points represent a relative minimum. (c) a horizontal point of inflection (-1; 2) (1' 5) (4' 1) -"'- None of these points represent a horizontal point of inflection. Use the indicated points on the graph of y = ((x) to identify points at which f(x) has a relative maximum, a relative minimum, and a horizontal point of inflection. 6- (1, 5) 4 (-1, 2) (4, 1) X -2 2 4 6 -2 (a) a relative maximum O (-1, 2) O (1, 5) O (4, 1) O None of these points represent a relative maximum.(b) changes from negative to positive O (-1, 3) O (2, 5) O (5, 7) O None of these points represents a change in f'(x) from negative to positive. (c) does not change sign O (-1, 3) O (2, 5) O (5, 7) Of'(x) does not change sign at any of these points.Use the indicated points on the graph of y = f(x) to identify points at which the derivative f'(x) changes from positive to negative, changes from negative to positive, and does not change sign. 7 (5, 7) (2, 5) 5/ 4 3 (-1, 3) 2 1 -3 -2 -1 X 1 2 3 4 5 6 7 -1 (a) changes from positive to negative O (-1, 3) O (2, 5) O (5, 7) O None of these points represents a change in f'(x) from positive to negative.Use the sign diagram for f'(x) to determine the following. (If an answer does not exist, enter DNE.) f (x) - - - 0+ + + + + 0 X (a) the critical values of f(x) (Enter your answers as a comma-separated list.) X = (b) intervals on which f(x) increases (Enter your answer using interval notation.) (c) intervals on which f(x) decreases (Enter your answer using interval notation.) (d) x-values at which relative maxima occur (Enter your answers as a comma-separated list.) X= (e) x-values at which relative minima occur (Enter your answers as a comma-separated list.) XConsider the following. y = 4x3 - 48x2 + 8 (a) Find the critical values of the function. (Enter your answers as a comma-separated list.) X = (b) Make a sign diagram and determine the relative maxima and minima. (If an answer does not exist, enter DNE.) relative maxima (x, y) = relative minima ( x, y ) =Consider the fa lowing. 12 -xx y 2 (a) Find y' - f'(x). f'(X) - (b) Find the critical value. x- (c) Find the critical point. (x.y)-( ) to] Find intervals of xvaiues where the function is increasing. (Enter your answer using Interval notation.) Find intervals of x-values where the function is decreasing. (Enter your answer using interval notation.) (e) Classify the critical point as a relative maximum, a relative minimum, or a horizontal point of inection. In each case, check your conclusions with a graphing utility. (If an answer does not exist, enter DNE.) relative maxima (x, y) - ( ) relative mlnima (x, y) - ( ) horizontal point of inflection (x, y) - ( ) Determine whether the function is concave up or concave down at the indicated points. g(x) = 2x4 - 5x3 + 15x - 4 (a) x = 3 O concave up O concave down (b) x = 2 O concave up O concave downConsider the function. g(x) = 2x4 - 4x3 + 15x - 3 Find g'(x). g'( x) = Find g"(x). g"(x) = Find g"(2) and g' g"(2) = Determine whether the function g(x) is concave up or concave down at the indicated points. (a) x = 2 O concave up concave down (b) x= O concave up O concave down