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please show step by step + (7) let f(x)= xe * Sketch f(x). Consider and local...
(8 pts) Let f(x) = xe-. Sketch a graph of this function using calculus, finding all relative extreme values and points of inflection. Use an appropriate scaling for the axes. Show and label all relevant features, including asymptotes, on your graph.
Problem 5. (15 pts) Consider f(x) = -1x + +8. (a) Find and classify all local extrema. Where is S(x) increasing? Decreasing? Justify your answer. (6) Find all inflection points. Where is f(x) concave up? Concave down? Justify your answer. (c) From the information above, sketch f(a).
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4) Graphing polynomials Sketch a graph of f(x) = x* + 4x3. (10 pts) D . C Not Secure Vizedhtmlcontent. next.ecollege.com d) Find critical points and possible inflection points. e) Find intervals on which the function is increasing/decreasing. f) Find intervals on which the function is concave up/down. g) Identify the local extrema.
Consider the function: f(x) = ln(cos x) Do the following: • Find the domain of the function • Find all critical points • Find all extrema and classify each as a local maximum, local minimum, or a saddle • Find all intervals of increase and decrease • Find all intervals of concavity and find any inflection points • Sketch a graph of the function with the information you found above
9. Determine where f(x) is increasing/decreasing. Locate the local extrema; determine where it is concave up/down, locate inflection pts. Use this information to sketch the graph. (20 pts) 4x2 + 12x – f'(x) = Critical Values are: F"(x) = Possible Inflection points are: First derivative information Interval Sample point f' = + or - Show inc/dec 2nd derivative information Interval Sample point f" x f" = + or - Concavity:
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2. Let f(x) = x* – 18x²+4. a) Find the intervals on which f is increasing or decreasing. b) Find the local maximum and minimum values off. c) Find the intervals of concavity and the inflection points. d) Use the information from a-c to make a rough sketch of the graph.
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2. Let f(x)=x* - 18x+4. a) Find the intervals on which f is increasing or decreasing. b) Find the local maximum and minimum values of f. c) Find the intervals of concavity and the inflection points. d) Use the information from a-c to make a rough sketch of the graph.
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(6 Let f(x) = (-1)" x 21 (2n)! Consider the even indexing show that f"(x) + f(x) = 0 powere of & when differentiating n=0 on the
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,
1 point) Sketch the graph of the function y = x(4-2) - 103 In x. Indicate the transition points (local extrema and points of inflection) (Use symbolic notation and fractions where needed. Give your answer in the form of comma separated list of e-coordinates. Enter NULL in answer field if there is no such point.) Local maximum at = help (fractions) Local minimum at I= Inflection at I= (1 point) Sketch the graph of the function y = 81x +...