Homework Answers
Show ALL work to receive rating. Thanks! 1. Let f(x) = -4x^3+6x^2 a) Where is f(x)...
Show ALL work to receive rating. Thanks! 1. Let f(x) = -4x^3+6x^2 a) Where is f(x) increasing/decreasing? Make a sign chart. b) Classify the critical points as local max, local min, or neither. c) Where is f(x) concave up/concave down? Does it have any points of inflection? d) Use the information above to sketch the curve. Note that f(1/2) = 1. Be sure your graph includes the x and y intercepts if they exist.
5. (13 pts) (x) = 2x° -6x° -18x a. Find the location of the local maximum(s)...
5. (13 pts) (x) = 2x° -6x° -18x a. Find the location of the local maximum(s) and minimum(s) off. You must show use of calculus. Use either the first derivative or second derivative test to prove they are maximum(s) or minimum(s). b. On what interval(s) is f(x) increasing? C. Use calculus to find and verify the location of any inflection points of f(x). d. On what interval(s) is f(x) concave up?
5) (From Hardcover Book, Marsden/Tromba, Vector Calculus, 6th ed., Exercises for Section 3.3, #34) Let f (x, y) еба — ....
5) (From Hardcover Book, Marsden/Tromba, Vector Calculus, 6th ed., Exercises for Section 3.3, #34) Let f (x, y) еба — . = 5ye* (a) Show that f has a unique critical point and that this point is a local maximum for f. (b) Show thatf is unbounded on the y-axis, and thus has no global maximum. (Note that for a differentiable function g (a) of a single variable, a unique critical point which is a local extremum is necessarily a...
5. Let f(x,y) = 3x2 y - y3 - 6x. (a) Find all the critical points...
5. Let f(x,y) = 3x2 y - y3 - 6x. (a) Find all the critical points off. (b) Classify each of the critical points; that is, what type are they? (c) For the same function f(x,y), find the maximum value of f on the unit square, 0 SX S1,0 <y s 1.
5. (10 points) Let f(x) = -(9x² +6x+2). Then according to the definition of derivative f'(x)...
5. (10 points) Let f(x) = -(9x² +6x+2). Then according to the definition of derivative f'(x) = lim h0 (Your answer above and the next few answers below will involve the variables x and h. We are using h instead of Ar because it is easier to type) We can cancel the common factor — from the numerator and denominator leaving the polynomial Taking the limit of this expression gives us f'(x) = 6. (10 points) Let f(x) = x3...
Let h(x) = 14), where f(x) = –2x – 3 and g(x) = x2 – x...
Let h(x) = 14), where f(x) = –2x – 3 and g(x) = x2 – x + 2. What is h' (x)? Select the correct answer below: 2x2 +6x–7 *4–2x3 +5x2–4x+4 -6x2–2x-1 x+-2x3 +5x2-4x+4 2x2+6x–7 x-x+2 O za
#1,2,4,5,7 Chapter 4 Functions of Two Variables Applied Calculus 272 4.3 Exercises For problems 1 through 6, find f/, f, and f, for the function given. Confirm that ух 3. f(t,y)-Sxy 4. f(x, y)-e&#...
#1,2,4,5,7
Chapter 4 Functions of Two Variables Applied Calculus 272 4.3 Exercises For problems 1 through 6, find f/, f, and f, for the function given. Confirm that ух 3. f(t,y)-Sxy 4. f(x, y)-e" 5.(x,y)-In(axy+2x-6y) y4-5 7. Find the critical points of f(x,y)-ys_x3 + 15x2-12y+12 and use the Second Derivative Test to classify them. If the test fails, say "the test fails. 3
Chapter 4 Functions of Two Variables Applied Calculus 272 4.3 Exercises For problems 1 through 6, find...
1) 2) Let f(x) = 23 + 9x² – 812 +21. (a) Use derivative rules to...
1)
2)
Let f(x) = 23 + 9x² – 812 +21. (a) Use derivative rules to find f'(x) = 3x2 +18% -81 (b) Use derivative or the derivative rules to find f''(x) = 60 + 18 (c) On what interval is f increasing (include the endpoints in the interval)? interval of increasing = (-0,-9] U [3,00) (d) On what interval is f decreasing (include the endpoints in the interval)? interval of decreasing = [-9,3] (e) On what interval is f...
Let f(x) 2x2 - 7x + 3 222 + 9x + 4 This function has: 1)...
Let f(x) 2x2 - 7x + 3 222 + 9x + 4 This function has: 1) A y intercept at the point Preview 2) x intercepts at the point(s) Preview 3) Vertical asymptotes at x = Preview Points possible: 1 This is attempt 1 of 1.
Given f(x) = x² - 6x² + 9 + 1 a) Find the intervals over which...
Given f(x) = x² - 6x² + 9 + 1 a) Find the intervals over which f(x) is increasing and decreasing. 6 Find any local maximum and minimum c) Find intervals over which the graph off is concave upward, and concave downward. Id Find any inflection points. e) Use the above results to graph FX).
5. (13 pts) (x) = 2x° -6x° -18x a. Find the location of the local maximum(s) and minimum(s) off. You must show use of calculus. Use either the first derivative or second derivative test to prove they are maximum(s) or minimum(s). b. On what interval(s) is f(x) increasing? C. Use calculus to find and verify the location of any inflection points of f(x). d. On what interval(s) is f(x) concave up?
5) (From Hardcover Book, Marsden/Tromba, Vector Calculus, 6th ed., Exercises for Section 3.3, #34) Let f (x, y) еба — . = 5ye* (a) Show that f has a unique critical point and that this point is a local maximum for f. (b) Show thatf is unbounded on the y-axis, and thus has no global maximum. (Note that for a differentiable function g (a) of a single variable, a unique critical point which is a local extremum is necessarily a...
5. Let f(x,y) = 3x2 y - y3 - 6x. (a) Find all the critical points off. (b) Classify each of the critical points; that is, what type are they? (c) For the same function f(x,y), find the maximum value of f on the unit square, 0 SX S1,0 <y s 1.
5. (10 points) Let f(x) = -(9x² +6x+2). Then according to the definition of derivative f'(x) = lim h0 (Your answer above and the next few answers below will involve the variables x and h. We are using h instead of Ar because it is easier to type) We can cancel the common factor — from the numerator and denominator leaving the polynomial Taking the limit of this expression gives us f'(x) = 6. (10 points) Let f(x) = x3...
Let h(x) = 14), where f(x) = –2x – 3 and g(x) = x2 – x + 2. What is h' (x)? Select the correct answer below: 2x2 +6x–7 *4–2x3 +5x2–4x+4 -6x2–2x-1 x+-2x3 +5x2-4x+4 2x2+6x–7 x-x+2 O za
#1,2,4,5,7
Chapter 4 Functions of Two Variables Applied Calculus 272 4.3 Exercises For problems 1 through 6, find f/, f, and f, for the function given. Confirm that ух 3. f(t,y)-Sxy 4. f(x, y)-e" 5.(x,y)-In(axy+2x-6y) y4-5 7. Find the critical points of f(x,y)-ys_x3 + 15x2-12y+12 and use the Second Derivative Test to classify them. If the test fails, say "the test fails. 3
Chapter 4 Functions of Two Variables Applied Calculus 272 4.3 Exercises For problems 1 through 6, find...
1)
2)
Let f(x) = 23 + 9x² – 812 +21. (a) Use derivative rules to find f'(x) = 3x2 +18% -81 (b) Use derivative or the derivative rules to find f''(x) = 60 + 18 (c) On what interval is f increasing (include the endpoints in the interval)? interval of increasing = (-0,-9] U [3,00) (d) On what interval is f decreasing (include the endpoints in the interval)? interval of decreasing = [-9,3] (e) On what interval is f...
Let f(x) 2x2 - 7x + 3 222 + 9x + 4 This function has: 1) A y intercept at the point Preview 2) x intercepts at the point(s) Preview 3) Vertical asymptotes at x = Preview Points possible: 1 This is attempt 1 of 1.
Given f(x) = x² - 6x² + 9 + 1 a) Find the intervals over which f(x) is increasing and decreasing. 6 Find any local maximum and minimum c) Find intervals over which the graph off is concave upward, and concave downward. Id Find any inflection points. e) Use the above results to graph FX).
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