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4 For the function f(x) = (x+3) (x-2) 3 the derivatives are f(x) = (5 x...
show all work, no written work f(x)= Vx? -2.Vx -3 Given: %3D a. Investigate the function...
show all work, no written work
f(x)= Vx? -2.Vx -3 Given: %3D a. Investigate the function by these criteria: 1) Domain; 2) Axis intersections; 3) Asymptotes (show the relevant limits) 4) Intervals of increase and decrease; 5) Points of relative extremum; 6) Intervals of concavity (upward or downward); 7) Inflection points. 8) Draw the function's graph. b. Find the equations of the tangent lines to the graph of the function at all extremum and inflection points, and add them to...
(x + 1)2 Consider the function f(x) -. The first and second derivatives of f(x) are...
(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...
Given the function f(x) and its derivative f'(x). F"(7), sketch the graph of f(x). If applicable,...
Given the function f(x) and its derivative f'(x). F"(7), sketch the graph of f(x). If applicable, identity local extremum, points of inflection, asymptotes, and intercepts. (1) f(a) == (2) f(x) = f(a) = (-1)"(t) = , f'(x) = -2° +8 f"(ar) = 24 (3) f(x) = (4) f(x) = r - 2 sin 2, 3 VI f'(x) = 1 - 2 cos z f"(x) = 2 sina,
2 (15 points) Given f(x) = Find the first and the second derivatives, and then graph...
2 (15 points) Given f(x) = Find the first and the second derivatives, and then graph (x + 1)2' f(x). Make sure to show all steps, label all your points, and clearly identify any critical points and inflection points.
Sketch the graph of the function f(x) - (2-6)(x+3) 9(2+2) A sketch need not be exact...
Sketch the graph of the function f(x) - (2-6)(x+3) 9(2+2) A sketch need not be exact or to scale! A sketch does need to show important points and features of the graph: intervals on which the function is increasing/decreasing, concavity, points at which local and absolute max, and min. values occur, inflection points, intercepts, vertical and horizontal asymptotes, and any other features particular to the particular function,
2. (a) Obtain and classify all stationary points and point of inflection of the function f(x)...
2. (a) Obtain and classify all stationary points and point of inflection of the function f(x) = 4x3 – 22x2 + 40x – 25. [5 marks) (b) Sketch the function y = f(x) showing all x and y intercepts, stationary points and point of inflection. One of the factors of f(x) = 423 – 22cr2 + 40x – 25 is (r – ). [2 marks] (c) Evaluate the definite integral of f(c) on the domain 2 € (0,6]. [3 marks)
for the function f(x) = 3x-x^3, find: 1) Domain 2) Intercepts (if possible) 3) Intervals of...
for the function f(x) = 3x-x^3, find: 1) Domain 2) Intercepts (if possible) 3) Intervals of increasing/decreasing and Relative max/min 4) Intervals of concavity and point of inflection 5) End behavior 6) Any vertical and horizontal asymptote 7) Use all the above to make a detailed graph of the function on a grid please write everything clearly and i'l rate you depending on the work, thanks.
A function and its first and second derivatives are given. Use these to find each of...
A function and its first and second derivatives are given. Use these to find each of the following. (If an answer does not exist, enter DNE.) f(x) = 12x2/3 x + 1 4(2-x) f'(x) = x1/3(x + 1)2 f"(x) = 8(2x2 - 8x - 1) 3x4/3(x + 1)3 Find any horizontal and vertical asymptotes. (Enter your answers as a comma-separated list of equations.) horizontal asymptotes vertical asymptotes Find any critical points. (x, y) = (0.0 (smaller x-value) (x, y) =...
just step 3 and 4 X-1 II. For f(x) find: x+3 Step 1: Analyze f(x) 4....
just step 3 and 4
X-1 II. For f(x) find: x+3 Step 1: Analyze f(x) 4. Domain 5. X-intercepts and y-intercepts (use calculator to approximate value. Round to two decimal places) 6. vertical and horizontal asymptotes (if exist) Step 2 Analyze f'(x) 6. critical points 7. intervals on which f(x) is increasing 8. intervals on which f(x) is decreasing 9. minimum, if exist 10. maximum, if exist Step 3 Analyze f"(x) 4. concavity upward 5. concavity downward 6. point(s) of...
5) The level curves of a function f(x,y) are given in the graph below. 2 X...
5) The level curves of a function f(x,y) are given in the graph below. 2 X -1 -2 i Estimate f(3,3) ii Estimate Vf(-3, 1) Let u be a unit vector parallel to (1,4). Calculate Daf using your answer from i iv) Find the location of all critical points of the function f, on the set -5 <r< of these is a saddle point) iii) Let D be the domain bounded between the curves y = x and y= 2...
show all work, no written work
f(x)= Vx? -2.Vx -3 Given: %3D a. Investigate the function by these criteria: 1) Domain; 2) Axis intersections; 3) Asymptotes (show the relevant limits) 4) Intervals of increase and decrease; 5) Points of relative extremum; 6) Intervals of concavity (upward or downward); 7) Inflection points. 8) Draw the function's graph. b. Find the equations of the tangent lines to the graph of the function at all extremum and inflection points, and add them to...
(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...
Given the function f(x) and its derivative f'(x). F"(7), sketch the graph of f(x). If applicable, identity local extremum, points of inflection, asymptotes, and intercepts. (1) f(a) == (2) f(x) = f(a) = (-1)"(t) = , f'(x) = -2° +8 f"(ar) = 24 (3) f(x) = (4) f(x) = r - 2 sin 2, 3 VI f'(x) = 1 - 2 cos z f"(x) = 2 sina,
2 (15 points) Given f(x) = Find the first and the second derivatives, and then graph (x + 1)2' f(x). Make sure to show all steps, label all your points, and clearly identify any critical points and inflection points.
Sketch the graph of the function f(x) - (2-6)(x+3) 9(2+2) A sketch need not be exact or to scale! A sketch does need to show important points and features of the graph: intervals on which the function is increasing/decreasing, concavity, points at which local and absolute max, and min. values occur, inflection points, intercepts, vertical and horizontal asymptotes, and any other features particular to the particular function,
2. (a) Obtain and classify all stationary points and point of inflection of the function f(x) = 4x3 – 22x2 + 40x – 25. [5 marks) (b) Sketch the function y = f(x) showing all x and y intercepts, stationary points and point of inflection. One of the factors of f(x) = 423 – 22cr2 + 40x – 25 is (r – ). [2 marks] (c) Evaluate the definite integral of f(c) on the domain 2 € (0,6]. [3 marks)
A function and its first and second derivatives are given. Use these to find each of the following. (If an answer does not exist, enter DNE.) f(x) = 12x2/3 x + 1 4(2-x) f'(x) = x1/3(x + 1)2 f"(x) = 8(2x2 - 8x - 1) 3x4/3(x + 1)3 Find any horizontal and vertical asymptotes. (Enter your answers as a comma-separated list of equations.) horizontal asymptotes vertical asymptotes Find any critical points. (x, y) = (0.0 (smaller x-value) (x, y) =...
just step 3 and 4
X-1 II. For f(x) find: x+3 Step 1: Analyze f(x) 4. Domain 5. X-intercepts and y-intercepts (use calculator to approximate value. Round to two decimal places) 6. vertical and horizontal asymptotes (if exist) Step 2 Analyze f'(x) 6. critical points 7. intervals on which f(x) is increasing 8. intervals on which f(x) is decreasing 9. minimum, if exist 10. maximum, if exist Step 3 Analyze f"(x) 4. concavity upward 5. concavity downward 6. point(s) of...
5) The level curves of a function f(x,y) are given in the graph below. 2 X -1 -2 i Estimate f(3,3) ii Estimate Vf(-3, 1) Let u be a unit vector parallel to (1,4). Calculate Daf using your answer from i iv) Find the location of all critical points of the function f, on the set -5 <r< of these is a saddle point) iii) Let D be the domain bounded between the curves y = x and y= 2...
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