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3. Suppose we estimateſ f(x)dx using our rules with the same number of subdivisions, n but...
1) 2) Let f(x) = 23 + 9x² – 812 +21. (a) Use derivative rules to...
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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...
Suppose that f(x)=ln(8x+6) (A) List all the critical values of f(x). Note: If there are no critic...
Suppose that f(x)=ln(8x+6) (A) List all the critical values of f(x). Note: If there are no critical values, enter 'NONE'. (B) Use interval notation to indicate where f(x)f(x) is increasing. Note: Use 'INF' for ∞, '-INF' for −∞, and use 'U' for the union symbol. If there is no interval, enter 'NONE'. Increasing: (C) Use interval notation to indicate where f(x) is decreasing. Decreasing: (D) List the xx values of all local maxima of f(x). If there are no local...
3. Consider the function f(x) = x2 - 6x^2 - 5 a. Find the values of...
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...
6. For a certain function f(x) we have: f'(x) = (x - 3)²(2x - 3) and...
6. For a certain function f(x) we have: f'(x) = (x - 3)²(2x - 3) and • f"(x) = 6(x - 3)(x - 2) (a) Use f' to find the intervals where f is increasing, the intervals where f is decreasing, the x- coordinates and nature (max, min or neither) of any local extreme values. (b) Use f" to find the intervals where the graph of f is concave up, the intervals where the graph of f is concave down...
4. For this question, define f(x) = (x - 1)e-(0-1). (a) Find f'(x) and f"(x). (b)...
4. For this question, define f(x) = (x - 1)e-(0-1). (a) Find f'(x) and f"(x). (b) Find where S is increasing and where / is decreasing (e) Find where S is concave up and where / is concave down. (a) Find all critical points of . For each point you find, explain whether it is a (relative) maximum, a (relative) minimum or neither. (e) Find all points of inflection of f. For each point you find, explain why it is...
Let f(x) = x 3 _ 3x² a) The interval(s) on which the function is increasing...
Let f(x) = x 3 _ 3x² a) The interval(s) on which the function is increasing and the intervalls) on which the function f is decreasing B) The relative maximum value of f is and the relative minimum value of f is c) The intervalls) on which the function of is and the intervalls) on concave up which the function F is concare down D) The inflection Point(s) off
(1 point) Suppose that f(x) = (??-9) (A) Find all critical values off. If there are...
(1 point) Suppose that f(x) = (??-9) (A) Find all critical values off. If there are no critical values, enter - 1000. If there are more than one, enter them separated by commas. Critical value(s) = (B) Use interval notation to indicate where f(x) is increasing. Note: When using interval notation in WeWork, you use I for 00,- for -00, and for the union symbol. If there are no values that satisfy the required condition, then enter ")" without the...
7. After sketching the graphs of function f(x) and its derivative f(x) on the interval [0, 10],I ...
7. After sketching the graphs of function f(x) and its derivative f(x) on the interval [0, 10],I spilled my tea on the graph of f(x). The coffee dissolved the ink as shown. Please redraw the graph for me using the graph of f(x). (Hint: Graph f"(x) to determine the concavity of the original graph.) Be sure to indicate important features like relative max and min, points of inflection, increasing and decreasing intervals, and intervals where the graph is concave up...
3. On the open interval (0, π/2), a function f with f'(x) = sin(x^2 ) must...
3. On the open interval (0, π/2), a function f with f'(x) = sin(x^2 ) must be (choose one, and explain your answer): (a) increasing and concave up (b) decreasing and concave up (c) increasing and concave down (d) decreasing and concave up (e) None of the above
1-Find the local maximum value of f using both the First and Second Derivative Tests. f(x)...
1-Find the local maximum value of f using both the First and Second Derivative Tests. f(x) = x + √4 - x 2-Consider the equation below. (If you need to use -∞ or ∞, enter -INFINITY or INFINITY.) f(x) = 2x3 + 3x2 − 72x (a) Find the intervals on which f is increasing. (Enter the interval that contains smaller numbers first.) ( , ) ∪ ( , ) Find the interval on which f is decreasing. ( , ) (b) Find the local minimum and...
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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...
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...
6. For a certain function f(x) we have: f'(x) = (x - 3)²(2x - 3) and • f"(x) = 6(x - 3)(x - 2) (a) Use f' to find the intervals where f is increasing, the intervals where f is decreasing, the x- coordinates and nature (max, min or neither) of any local extreme values. (b) Use f" to find the intervals where the graph of f is concave up, the intervals where the graph of f is concave down...
4. For this question, define f(x) = (x - 1)e-(0-1). (a) Find f'(x) and f"(x). (b) Find where S is increasing and where / is decreasing (e) Find where S is concave up and where / is concave down. (a) Find all critical points of . For each point you find, explain whether it is a (relative) maximum, a (relative) minimum or neither. (e) Find all points of inflection of f. For each point you find, explain why it is...
Let f(x) = x 3 _ 3x² a) The interval(s) on which the function is increasing and the intervalls) on which the function f is decreasing B) The relative maximum value of f is and the relative minimum value of f is c) The intervalls) on which the function of is and the intervalls) on concave up which the function F is concare down D) The inflection Point(s) off
(1 point) Suppose that f(x) = (??-9) (A) Find all critical values off. If there are no critical values, enter - 1000. If there are more than one, enter them separated by commas. Critical value(s) = (B) Use interval notation to indicate where f(x) is increasing. Note: When using interval notation in WeWork, you use I for 00,- for -00, and for the union symbol. If there are no values that satisfy the required condition, then enter ")" without the...
7. After sketching the graphs of function f(x) and its derivative f(x) on the interval [0, 10],I spilled my tea on the graph of f(x). The coffee dissolved the ink as shown. Please redraw the graph for me using the graph of f(x). (Hint: Graph f"(x) to determine the concavity of the original graph.) Be sure to indicate important features like relative max and min, points of inflection, increasing and decreasing intervals, and intervals where the graph is concave up...
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