Let f(x)=3x-7/x+2. Find the open intervals on which f is concave up (down). Then determine the x-coordinates of all inflection points of f. Let Find the open intervals on which is concave up down Then determine the X-coordinates of all inflection points of x = f is concave up on the intervals 1. 2. f is concave down on the intervals 3· The inflection points occur at Notes: In the first two, your answer should either be a single interval,...
6. For a certain function f(x) we have: f'(x) = (x - 3)²(2x - 3) and • f"(x) = 6(x - 3)(x - 2) (a) Use f' to find the intervals where f is increasing, the intervals where f is decreasing, the x- coordinates and nature (max, min or neither) of any local extreme values. (b) Use f" to find the intervals where the graph of f is concave up, the intervals where the graph of f is concave down...
Q-5: [5x1 marks] Let f(x) = 10 + (x – 2)4 a) Find f'(x) and f'(x). b) Find the intervals on which f is increasing or decreasing. c) Find the local maximum and minimum of f, if any. d) Find the intervals on which the graph of f is concave up or concave down. e) Find the points of inflection, if any.
(x + 1)2 Consider the function f(x) -. The first and second derivatives of f(x) are 1 + x2 2(1 – x2) 4x(x2 - 3) f'(x) = and f" (2) Using this information, (1 + x2) (1 + x2)3 (a) Find all relative extrema. (4 points) Minimum: Maximum: (b) Find the intervals of concavity for f(x) and identify any inflection points for yourself. (5 points) Concave up: Concave down: (c) Using the fact that lim f(x) = 1, and our...
conisder the following function: a)Find the x-intervals on which the graph of f is concave up, and where it is concave down b)Identify any inflection points on the graph of F. f(x) = 23 – 9x2 - 4
5.1 - 2 (2 points) Let f(x) Find the open intervals on which f is concave up (down). Then determine the e-coordinates of all inflection points of 2 + 7 1. f is concave up on the intervals 2. f is concave down on the intervals 3. The inflection points occur at 2 - Notes: In the first two, your answer should either be a single interval, such as (0,1), a comma separated list of intervals, such as (-int, 2),...
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.
5 For the functions f(x) = (2,2 – 2x)e- and g(x) = 2.5 – 3.23 + 22:2 (1) dentify and classify any stationary points using the second derivative test. (1) Identify and classify any points of inflection using the sign diagram of the second deriva- tive, (i) Determine the intervals where the function is concave up and concave down.
. Find the intervals on which f(x) = x^4 + 2x^3 − 36x^2 + 9x − 47 is concave down and up, along with the x-coordinates of any inflection points. Justify all your work
Question 11 10 pts The derivative f'(2) of an unknown function f(x) has been determined as f'(x) = (x - 2)(+3)2. Use this derivative to find the intervals where the original function f is increasing/decreasing. Then find the x-values that correspond to any relative maximums or relative minimums of the original unknown function f(x). O no relative maximum; relative minimum at x=2 relative maximum at x=-3; no relative minimum O relative maximum at x=2; relative minimum at x=-3 relative maximum...