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(1 point) Find the maximal and minimal values for the function f(x) = x4 – 4x3...
5. Given the function f(x)=x4 - 4x3 a) find f'(x) and the critical numbers of f. b) determine the interval(s) on which the graph off is increasing c) find f"(x) and the x-coordinates of the possible inflection points d) determine the interval(s) on which the graph off is concave down.
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The function defined by f(x) = x4 + 4x3 - 16x2 - 64x has the graph, as shown. 200- X Use the graph to factor the polynomial. 7 -200 What is the factored form of the polynomial? f(x) = (Simplify your answer. Type your answer in factored form.) Graph the polynomial function f(x) = 2x3 X° + 1. Then answer parts a and b. Choose the correct graph below. O A. OB O c. OD У AY...
2. (10 points) For function f(x) = 4x3 – x4, find: (a) the critical points; (b) the open intervals on which the function is increasing or decreasing; (c) locate all relative extrema.
Find the average rate of change for the following function. f(x) = 4x3 – 5x2 + 7 between x = - 2 and x = 3 The average rate of change for f(x) over the interval - 2 to 3 is (Type an integer or a simplified fraction.)
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2. (10 points) For function f(x) = 4x3 – x4, find: (a) the critical points; (b) the open intervals on which the function is increasing or decreasing; (c) locate all relative extrema.
Find the average rate of change for the following function. f(x) = 4x3 - 2x + 7 between x= -1 and x = 2 . The average rate of change for f(x) over the interval - 1 to 2 is (Type an integer or a simplified fraction.)
Find the derivative of the function. F(x) = (x4 + 3x2 - 2) F'(x) F(x) = Find the derivative of the function. f(x) = (3 + x)2/ f'(x) = Find the derivative of the function. g(t) = 7+4 + 4)5 g'(t) =
3. Consider the function f(x) = x2 - 6x^2 - 5 a. Find the values of x such that f'(x) = 0. b. Use the results of part a to: find interval(s) on which the function is increasing and interval(s) on which it is decreasing. c. Find the value(s) of x such that f"(x)=0. d. Use the result of part c to find interval(s) on which f(x) is concave up and interval(s) on which it is concave down. e. Sketch...
Find the average rate of change for the following function. f(x) = 4x3 - 5x2 +6 between x = -2 and x = 1 The average rate of change for f(x) over the interval - 2 to 1 is (Type an integer or a simplified fraction.)
Find the second derivative of the function. y = 4(x2 + 2x)3 y" = _______ Find the third derivative of the function. f(x) = x4-4x3 f'''(x) = _______