Consider the following. f(x) = - *** + 3x3- 1/3 - 3x2 + 8 Find f'(x). f'(x) = Find F"(x). f"(x) = Find the x-values of the possible points of inflection. (Enter your answers as a comma-separated list.) X = Determine the intervals on which the function is concave up. (Enter your answer using interval notation.) Determine the intervals on which the function is concave down. (Enter your answer using interval notation.) Locate the points of inflection. (If an answer...
Consider the following. f(x) = 1 4 x4 + 1 2 x3 − 3x2 + 4 Find f '(x). f '(x) = x3+ 3x2 2−6x Find f ''(x). f ''(x) = 3x2+3x−6 Find the x-values of the possible points of inflection. (Enter your answers as a comma-separated list.) x = Determine the intervals on which the function is concave up. (Enter your answer using interval notation.) Determine the intervals on which the function is concave down. (Enter your answer using...
12. Determine the intervals on which the function f(x) = 3x5 - 10x3 + 12x - 5 is concave up or concave down and identify any inflection points. Write intervals in interval notation.
ESTION 6 (8 marks) Consider the function f(x) = 2 2+1 .) Find the interval(s) in which the function f(x) is increasing and the interval(s) in which the function is decreasing. b) Find the interval(s) in which the function f(x) is concave up and the interval(s) in which the function is concave down. c) Sketch the graph of the function f(x) ABC T T Arial 3 (12pt) T
Find the inflection points. Find the interval on which f is concave up. Find the interval on which f is concave down. Step 1 We have f'(x) = 4 cos(x) – 4 sin(x), so f"(x) = -4 cos (x) – 4 sin (x) - 4 sin(x) – 4 cos(x) which equals 0 when tan(x) = -1 Hence, in the Interval o <x< 211, f'(x) = 0 77 when X = 371 4 7 л 4 and x = Step 2...
What are the x-coordinate(s) of the x-intercept(s) of the function? g(x)4x3 2x2 -12x
What are the x-coordinate(s) of the x-intercept(s) of the function? g(x)4x3 2x2 -12x
19. f(x)=4x3- 15x2 18x+ 20 3 (a) Find f'(x) Simplify and factor completely. )12x- 3ox-18 Find f(x) (b) Simplify and factor completely. ( 1.F Intevas are 242-30 (c) Find the intervals where the function is increasing and where it is decreasing. Use interval notation. : 24y-30 O 12 -30x-18O ,3 (-0,). 3). 39 -15 12 3 C 3, 00) 24 -) f is INC on: f is DEC on: Chrek Find the relative extrema of this function if they exist....
1-Find the local maximum value of f using both the First and Second Derivative Tests. f(x) = x + √4 - x 2-Consider the equation below. (If you need to use -∞ or ∞, enter -INFINITY or INFINITY.) f(x) = 2x3 + 3x2 − 72x (a) Find the intervals on which f is increasing. (Enter the interval that contains smaller numbers first.) ( , ) ∪ ( , ) Find the interval on which f is decreasing. ( , ) (b) Find the local minimum and...
For g(x) = 3x2-12x + 6, answer the following questions. a. Find the values of the x-intercepts b. State the coordinates of the y-intercept. c. State the vertex d. State the axis of symmetry e. State the direction of the parabola. f. Decide whether there is a relative maximum or minimum, then state it. g. Graph the function accurately using the above information. h. State the domain. i. State the range. j. State the interval of x where the graph is increasing k. State the interval of x where the graph...
22:13 edfinity.com 1. Find the open interval(s) on which f is concave upward. Answer (in interval notation): 2. Find the open interval(s) on which f is concave downward. Answer (in interval notation): 3. Find the coordinates of the points of inflection. List your answers as points in the form (a, b). Answer separate by commas):