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Part IV: Applications Consider this function, along with its derivative and its seco derivative: 48(16 + 3r2 У -(...
2. (20 pts) Consider the following function with its second derivative in simplified form (you should compute the first derivative): 4.2 f(x) = x²+1 f"(x) = 8.2(x - 3)(x + 3) (x² + 13 "None" could be an appropriate answer for some of the statements below: (a) (2 pts) The domain of f(x) is (b) (2 pts) An x-intercept of the graph of y = f(x) occurs at x = (c) (2 pts) The graph of y = f(x) has...
QUESTION 8 Find the equation(s) of all vertical and horizontal asymptotes for the function f(x) = (5x + 2)(3x-2) x² - 16 Vertical Asymptote(s): X = - Horizontal Asymptote(s): y = 15 Vertical Asymptote(s): X = -4,x = 4: Horizontal Asymptote(s): None Vertical Asymptote(s): X = -4,x = 4: Horizontal Asymptote(s): y = 15 лм am Vertical Asymptote(s): X= -4,x = 4: Horizontal Asymptote(s): y = Vertical Asymptote(s): X UN 5 Horizontal Asymptote(s): None
r2 Consider the function f(x) x2 - 9 For the following questions, write inf for 0, -inf for -00, U for the union symbol, and NA (ie. not applicable) if no such answer exists. a.) f'(x) = b.) f(x) is increasing on the interval(s) c.) f(x) is decreasing on the interval(s) d.)f(x) has a local maximum at e.)f(x) = f.)f(x) is concave up on the interval(s) 9.)f(x) concave down on the interval(s) h.) f(x) has a horizontal asymptote y =...
Can please help on how to simply the derivative I get lost on part c Name: (3) Consider the graph of the function 5e-3 (a) Find the z- and y-intercepts of the graph, if any. The answers are equa f(z) = tions, not numbers. (b) Find the horizontal and vertical asymptotes of the graph, if any. The answers are equations, not numbers. (c) Where is f(x) increasing? ...decreasing? The answers are intervals. (d) Where is f(x) concave up? concave down?...
f(T) = 22 9 Instructions: • If you are asked for a function, enter a function. • If you are asked to find 2- or y-values, enter either a number or a list of numbers separated by commas. If there are no solutions, enter None. • If you are asked to find an interval or union of intervals, use interval notation. Enter { } if an interval is empty • If you are asked to find a limit, enter either...
15-16 The graph of the derivative f' of a continuous function f is shown. (a) On what intervals is f increasing? Decreasing? (b) At what values of x does f have a local maximum? Local minimum? (c) On what intervals is f concave upward? Concave downward? (d) State the x-coordinate(s) of the point(s) of inflection. (e) Assuming that f(0) = 0, sketch a graph of f. 15. y A y = f'(x) --2 0 2 6 8 x -2
a-i pls thank you 13. A function is given below along with both its first and second derivatives. f(x) 2x+4 2x+3 (x+1) 4x+10 Find the following for this function: (a) the domain (b)x and y-intercepts (c) vertical anf horizontal asymptotes (d) critical numbers (e) intervals of increase and/or intervals of decrease (1) local extreme values (2) inflection points (h) intervals of concave up and concave down (1) graph the function and carefully label the y-intercept, local extrema, and point(s) of...
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 8 (20 points) Use the function g( 3 40-16 Yon to answer the following questions 1) The equation(s) of the vertical asymptote(s). If there are multiple vertical asymptotes, enter commas between the equations, no spaces. If no vertical asymptotes exist, enter "none". 2) The value of x of any holes in the graph. If multiple holes exist, enter commas between the values, no spaces. If no holes exist, enter "none". 3) The equation(s) of the horizontal asymptote(s). 3) The...
Consider the function below. f(x) = x^2 / ( x - 8 ) ^2 (a) Find the vertical and horizontal asymptotes. x= y= (b) Find the interval where the function is increasing. (Enter your answer using interval notation.) Find the interval where the function is decreasing. (Enter your answer using interval notation.) (c) Find the local minimum value. (d) Find the inflection point. (x, y) = e :Find the interval where the function is concave up. (Enter your answer using...