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Homework 06B: Problem 5 Previous Problem Problem List Next Problem (1 point) Consider the function f(x) = -2x3 + 21x2 - 36x + 5. (a) Find all critical numbers coff. c = (b) f is increasing for T E (c) f is decreasing for I E Note: Input U, infinity, and -infinity for union, oo, and -oo, respectively. If there are multiple answers, separate them by commas. If there is no answer, input none.Homework 06B: Problem 11 Previous Problem Problem List Next Problem (1 point) Consider the function f(x) = -4x2 + 8x - 7. (a) Find all critical numbers coff. c = (b) The local maxima values of f are: (c) The local minima values of f are: Note: If there are multiple answers, separate them by commas. If there is no answer, input none.Homework 06B: Problem 4 Previous Problem Problem List Next Problem (1 point) Find all critical numbers c of f(r) = 16x Inc. C = Note: If there is more than one critical number, separate them by a comma.Homework 06B: Problem 2 Previous Problem Problem List Next Problem (1 point) Suppose y = (x2 + 8)3. (a) Find the differential: dy dr. (b) Compute the differential when x = 1 and de = 0.05: dy =Homework 06B: Problem 10 Previous Problem Problem List Next Problem (1 point) Consider the function f(x) = 8x2 - 2x4 (a) f is increasing for I E (b) f is decreasing for I E (c) The relative maxima of f occur at c = (d) The relative minima of f occur at c = Note: Input U, infinity, and -infinity for union, oo, and -oo, respectively. If there are multiple answers, separate them by commas. If there is no answer, input none.Homework 06B: Problem 9 Previous Problem Problem List Next Problem (1 point) Consider the function f(x) = 67-2 x - 6 (a) f is increasing for I E (b) f is decreasing for I E (c) The local maxima of f occur at c = (d) The local minima of f occur at r = Note: Input U, infinity, and -infinity for union, oo, and -oo, respectively. If there are multiple answers, separate them by commas. If there is no answer, input none.Homework 06B: Problem 12 Previous Problem Problem List Next Problem (1 point) Consider the function f(x) = 2x + 5x-1 (a) f has a relative maximum at the point ( (b) f has a relative minimum at the point (Homework 06B: Problem 7 Previous Problem Problem List Next Problem (1 point) Consider the graph of f() given below. (a) Analyzing the graph, if g(x) = f(x), then g is decreasing for T E (b) Analyzing the graph, if h'(x) = f(x), then h is decreasing for I E Note: Input U, infinity, and -infinity for union, oo, and -oo, respectively.Homework 06B: Problem 8 Previous Problem Problem List Next Problem (1 point) Consider the function f(x) = -6x3 + 27x2 + 504x - 4. (a) f is increasing for I E (b) f is decreasing for I E (c) The local maxima of f occur at c (d) The local minima of f occur at c = Note: Input U, infinity, and -infinity for union, oo, and -oo, respectively. If there are multiple answers, separate them by commas. If there is no answer, input none.Homework 06B: Problem 13 Previous Problem Problem List Next Problem (1 point) Find all critical numbers c of f(2) = (7x +6)e 2:. C Note: If there is more than one critical number, separate them by a comma.Homework 06B: Problem 6 Previous Problem Problem List Next Problem (1 point) Consider the graph of f() given below. (a) Analyzing the graph, if g(x) = f(x), then g(x) is increasing for I E (b) Analyzing the graph, if h'(x) = f(x), then h(x) is increasing for T E Note: Input U, infinity, and -infinity for union, oo, and -oo, respectively. Clicking on the graph will enlarge it. Each tick on the graph is 1 unit.Homework 06B: Problem 3 Previous Problem Problem List Next Problem (1 point) Find all critical numbers c of f() = -2x- + 4x - 169. Note: If there is more than one critical number, separate them by a comma