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Question 17 5 pts Suppose f(x) = [Vť – 5t + 6.25 dt. For which positive...
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...
allowed time frame. Question 11 4 pts Find the derivative of the function. x3 f(x) = In X X3 O 3x2 x3-2 O 3x2-1 x(x3 - 2) O 2x3 + 2 x(x3 - 2)
5. Letf(x) = x3 + x2 - x - 1. a. 6 pts Find all critical values off. Show all work. Answers from a graph will not receive full credit. b. 6 pts Make a sign chart for f'(x). c. 4 pts List the x and y coordinates of all local maxima and minima on the graph off. Clearly identify if the point is a maximum or minimum. d. 6 pts Make a sign chart for f'(x). e. 4 pts...
17. Given the following function and its first and second derivative: 20-2 6-43 f'(x)= f"(x) = [2 pts] 1) Find the horizontal and vertical asymptotes of f(x), if any. f(x)=x-2x=1 نر [2 pts) ii) Find all critical numbers. Note: NOT a point, just critical numbers only. [5 pts) iii) Find the intervals of increasing and decreasing then finding all local maximum minimum values. [5 pts] Find the intervals of concave upward and concave downward. [2 pts) Find inflection point, if...
Question 13 4 pts Solve the problem. Find F '(x) if Flx)= dt Question 14 4 pts Find the domain and range and describe the level curves for the function f(xy). fix. y)-25-2 O Domain all points in the xy-plane; range real numbers 0szs S; level curves: circles with centers at (0.0) and radi r,0<rs5 Domain all points in the xy-plane satistyingx2 y2s25;range: real numbers 0 szs 5: level curves: circles with centers at (0.0) and radi r. 0crs5 O...
Question 1. (15 pts) Given f(x, y) = 3x 2 + y 3 . (a) Find the gradient of f. (b) Find the directional derivative of f at P0 = (3, 2) in the direction of u = (5/13)i + (12/13)j. Question 1. (15 pts) Given f(L,y) = 3x2 +y?. (a) Find the gradient of f. (b) Find the directional derivative off at P =(3,2) in the direction of u=(5/13)i + (12/13)j.
S o mo (StS 4. (20 pts) Analyze the graph of f(x) = 2x + 3x2 - 12x +1. fo.6x246-12 a. Use technology to find the x-and y-intercepts. (Round to two decimal places.) x Int (-3.34,0), (0.09.0) (1.76, u) yint 10.1) b. Find all the stationary points. If none, write NONE. +x) - 6x2 +6 Y-12 0.6*26* 2 8 1 -2 C. Use the first derivative test to determine if the stationary points are relative maxima, minima or neither. f(-3)...
Question 1 1 pts Look at following graph which is graph of function y = f(x). Using the graph how many inflection points does f(x) has? 1.5 1 0.5 -1.5 -1 -0.5 0.5 1 1.5 2 2.5 3 3.5 -0.5 1 a 2 O
2. f(x) = x? – 3x² +5. a) (5 pts) Find the (x, y) coordinates of the critical points. b) (5 pts) Find the (x, y) coordinates of the point of inflection (point of diminishing return) c) (5 pts) Over what interval is the function increasing/decreasing and over what interval is the function concave up/concave down? Analytically test for concavity. d) (5 pts) Use the 2nd derivative test to determine (x, y) coordinates of the relative max/min.
1.8 pts D Question 5 Referring to the graph shown, rank the following quantities: f(x)da, L-f(x)dx, &* f(x)dz, Sf(x)dz, and 0 S f()da < Sf(r)dx < L. f(x)dx < Sf(x)dx < 0 f(x)dx < $(x)dx <O<f()dx <S f(x)da of(x)d« <L. f(x)dx <O<S f(x)dx < 8 f(x)dt S f()dx < Sf(x)dx < 0< . f(x)dx < Sf(x)da f(x)d« <S f(x)dx < 0<S f(x)d« < $*f(x)da Question 6