Critical points of f(x) are (If there is more than one critical point, enter a comma-separated list. If there are no critical points, "none".) f(x) is increasing on f(x) is decreasing on (Enter your answers using interval notation.) f(x) has local maxima at f(x) has local minima at (If there is more than one extremum of a given tyne enter a coomma-senarated list If there are no
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The derivative of ?(?) is given by ?′(?)=(3−?)(?+4)/(?−4)(?+3). Find the critical points and local extrema of ?, and the open intervals on which ? is increasing and decreasing. (Assume that ?(?) and ?′(?) have the same domain.)
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- In the function: f(x)= (4x^2)/((x^2)+4) What are the critical numbers of the function? Where is the function increasing and decreasing in interval notation? What are the x-coordinates of all local minima and local maxima?Suppose that f(x)=(2x)/(x^2-4) (A) Find all critical values of f, compute their average, and enter it below. Note: If there are no critical values, enter -1000. Average of critical values =__________________ (B) Use interval notation to indicate where f(x) is increasing. Increasing:_______________ (C) Use interval notation to indicate where f(x) is decreasing. Decreasing:__________________ (D) Find the x-coordinates of all local maxima of f, compute their average, and enter it below. Note: If there are no local maxima, enter -1000. Average of x values =______________________ (E) Find the x-coordinates of all local minima of f, compute their average, and enter it below. Note: If there are no local minima, enter -1000. Average of x values =___________________ (F) Use interval notation to indicate where f(x) is concave up. Concave up: _____________________ (G) Use interval notation to indicate where f(x) is concave down. Concave down:____________________ (H) Find all inflection points…Suppose that f(x)=7x^2ln(x), x>0 (A) Find all critical values of f, compute their average, and enter it below. Note: If there are no critical values, enter -1000. Average of critical values =___________________ (B) Use interval notation to indicate where f(x) is increasing. Increasing: ________________________ (C) Use interval notation to indicate where f(x) is decreasing. Decreasing:___________________ (D) Find the x-coordinates of all local maxima of f, compute their average, and enter it below. Note: If there are no local maxima, enter -1000. Average of x values =___________________ (E) Find the x-coordinates of all local minima of f, compute their average, and enter it below. Note: If there are no local minima, enter -1000. Average of x values =_________________ (F) Use interval notation to indicate where f(x) is concave up. Concave up:_________________ (G) Use interval notation to indicate where f(x) is concave down. Concave down:_____________________ (H) Find all inflection…
- Given the function f(x)= x^4 - 4x^3, (a) find the domain of function f and x-intercepts, y-intercepts. (B) Find all critical numbers of f and show where f Is increasing or decreasing (c) Find all possible inflection number (if any) and show where the graph is concave up or concave down (d) Classify all points at critical numbers as local maximum points, local minimum points, or neither.In the function: f(x)=(12−3x)e^x What are the critical numbers of the function? When is the function increasing and decreasing in interval notation? What are the x-coordinates of all local minimums and maximums?Find the absolute maximum and minimum points, if they exist, of f(x)=x3+x2-x+1 the interval [-2, 1/2] show work to find all critical points in the interval
- Find the location of the global maximum and minimum of f(x) = x^3-6x^2+1f(x)=x3−6x2+1 on the interval [-1,7][−1,7]. a) The global maximum is attained at x = 0x=0 and the global minimum at x = 4x=4. b) The global maximum is attained at x = 7x=7, but there is no global minimum. c) The global maximum is attained at x = 0x=0 and the global minimum at x = -1x=−1. d) The global maximum is attained at x = 0x=0, but there is no global minimum. e) The global maximum is attained at x = 7x=7 and the global minimum at x = -1x=−1. f) The global maximum is attained at x = 7x=7 and the global minimum at x = 4x=4.Suppose that f(x)=10x−5ln(x), x>0 (A) Find all critical values of f, compute their average, and enter it below. Note: If there are no critical values, enter -1000. Average of critical values =__________________ (B) Use interval notation to indicate where f(x) is increasing.Increasing: ________________ (C) Use interval notation to indicate where f(x) is decreasing. Decreasing: ___________________ (D) Find the x-coordinates of all local maxima of f, compute their average, and enter it below. Note: If there are no local maxima, enter -1000. Average of x values =______________________. (E) Find the x-coordinates of all local minima of f, compute their average, and enter it below. Note: If there are no local minima, enter -1000. Average of x values =_________________ (F) Use interval notation to indicate where f(x) is concave up. Concave up: _________________ (G) Use interval notation to indicate where f(x) is concave down. Concave down: ___________________ (H) Find all inflection…a. Find the critical points of f(x)=x^3-12x-5 and identify the open intervals on which f is increasing and on which f is decreasing b. find lim x arrow infinity (1+1/x)^x
- In the function: f(x)= 6/((x^2)-16) What are the critical numbers of the function? When is the function increasing and decreasing in interval notation? What are the x-coordinates of all local minima and maxima?Find the critical numbers and the open intervals on which the function is increasing or decreasing. y = x3 − 12x + 2Find and classify the critical points off(x)=4x^6(2−x)^7 as local maxima and minima.Critical points: x= Classifications: (Enter your critical points and classifications as comma-separated lists, and enter the types in the same order as your critical points. Note that you must enter something in both blanks for either to be evaluated. For the types, enter min, max, or neither.