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How do you do this problem? 3. Let h be a function whose first derivative is...
is: 6. (8 points) / is a function that is continuous on (-0,00). The first derivative of /"(x) = (3x - 1)x+3X5 - x) Use this information to answer the following questions about : a. On what intervals is increasing or decreasing? Internal in which fis increasing or -- 8x-1) (x+3)(5-x) > 0 x=112, -3, -5 b. At what values of x does f have any local maximum or minimum values? - V2 ; Location(s) of Minima: Location(s) of Maxima:...
Let f(x) = 3r" +44.23 + 204r? + 288. - 3. Calculate the derivative f'(x) = Calculate the second derivative f''(x) Note intervals are entered in the format (-00,5)U(7,00) (these are two infinite intervals). Enter "DNE" if the interval is empty. On what interval(s) is f increasing? Increasing: On what interval(s) is f decreasing? Decreasing: On what interval(s) is f concave downward? Concave Down: On what interval(s) is f concave upward? Concave Up: What is the limit as x approaches...
4. Accurately apply each of the following to hx)-12x3-36x1+3 (5 points each): a) Intervals where h(x) is increasing/decreasing b) The first derivative test for local maxima and minima c) Intervals where h(x) is concave up/concave down d) The second derivative test for local maxima and minima 4. Accurately apply each of the following to hx)-12x3-36x1+3 (5 points each): a) Intervals where h(x) is increasing/decreasing b) The first derivative test for local maxima and minima c) Intervals where h(x) is concave...
The graph of y = f'(x), the derivative of a function f. 600,00) is given below: y= f'() Which of the following must be true? of is decreasing on (2, 4) and concave down on (-3,3). of is increasing on (-2, 2) and concave down on (0,4). f is increasing on (-3,0) and concave down on (0,4). fis decreasing on (0,4) and concave down on (-2,2).
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...
2. for the function f(x)= x+2 cos x on the interval [0,2pi] a. find the first derivative b.) find the second derivative c.) find the functions critical values(if any). include their y- coordinates in your answers in order to form critical points. d. )find the intervals on which f is increasing or decreasing. e. )find the local extrema of f. f. )find the functions hyper critical values(if any). include their y coordinates g.) find the intervals of concavity, i.e. the...
An object moves up and down. Its height, h in feet, is a function of time, t in seconds. It is known that • The domain is (-2,4). • The initial height is h(0) = 7 feet. • The graph of the velocity is h' (ft/s) 12 А. t(s) 1 -8 -12 1. What intervals is the height is increasing or decreasing? Enter answers using interval notation. Enter multiple intervals as comma-separated list. increasing (0.2) decreasing (-2,0), (2, 4) 2....
Q2) a) b) c) Name: (15 pts) Consider the function f (x) whose first derivative is f'(x) = 10x + 8 sec(x) tan(x). If f(0) = 3, what is f(x)? (5 pts each) The graph of g consists of two straight lines and a semi-circle. Let A(x) = (*g(t)dt and evaluate the following. a) A(4) у 8 6 + 2 X 0 6 8 -27 semi-circle b) A(8) c) A' (7)
5. This problem concerns a function , about which the following information is known . fis a differentiable function defined at every real number x. y-f'(x) has its graph given in the middle picture below S. This problem concerns a function f, about which the following information is f is a differentiable function defined at every real number x. y(x) has its graph given in the middle picture below. Construct a first derivative sign chart for f. Clearly identify all...
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...