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y = x^2 / x-5
graph the function
-identify the domain and any symmetries
-find the derivatives y' and y"
-find the critical points and identify the function's behavior at each one
-find where the curve is increasing and where it is decreasing,
-find the points of inflection
-determine the concavity of the curve
-identify any asymptotes
-find the coordinates of absolute extreme points, if any
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- 1.Identify the kind of function. 2.Find the x- and y- intercepts and the vertical abs horizontal asymptotes. 3.Find the end behavior of the function (y,y)find the inflection points (if any) on the graphof the function and the coordinates of the points on the graph wherethe function has a local maximum or local minimum value. Then graphthe function in a region large enough to show all these points simultaneously.Add to your picture the graphs of the function’s first andsecond derivatives. How are the values at which these graphs intersectthe x-axis related to the graph of the function? In what other ways arethe graphs of the derivatives related to the graph of the function? y = x3 - 12x2a) The equation of the horizontal asymptote. b) A critical point.
- a. Locate the critical points of ƒ.b. Use the First Derivative Test to locate the local maximum and minimumvalues.c. Identify the absolute maximum and minimum values of the functionon the given interval (when they exist). ƒ(x) = x - 2 tan-1 x on [-√3, √3]Find all the critical points and horizontal and vertical asymptotes of the function f(x)=(x^2+5)/(x-2). Use the First and/or Second Derivative Test to determine whether each critical point is a local maximum, a local minimum, or neither. You may use either test, or both, but you must show your use of the test(s). You do not need to identify any global extrema.find the inflection points (if any) on the graph ofthe function and the coordinates of the points on the graph where thefunction has a local maximum or local minimum value. Then graph the function in a region large enough to show all these points simultaneously. Add to your picture the graphs of the function’s first and secondderivatives. How are the values at which these graphs intersect thex-axis related to the graph of the function? In what other ways are thegraphs of the derivatives related to the graph of the function?129. y = x5 - 5x4 - 240 130. y = x3 - 12x
- Find an absolute minimum and absolute maximum,find a local minimum and local maximum, find the second derivative, and find the point of inflection show all work y= x-sinx, 0 less than or equal to x less than or equal to 2pieFind the exact x-value where the function f(x) = x + ln (x2 -1) attains a maximum value. Please donot provided the answer from the graph or estimation. Please show the process.Find the x-coordinates of all critical points of the given function. Determine whether each critical point is a relative maximum, a relative minimum, or neither, by first applying the second derivative test, and, if the test fails, by some other method. g(x) = 2x3 − 24x + 8 Step 1 Recall that a critical point is any interior point x in the domain of f where f '(x) = 0 or f '(x) is not defined. To find the critical points of g(x), first find the first derivative g'(x). Since g(x) = 2x3 − 24x + 8, then g'(x) = x2 − 24.
- 1/(x2 - 4) Use the following function along with its first and second derivatives to do the following: A. Find the intervals of increase and decrease and use the critical numbers to find the local max and minimums. B. Find the Concavity C. Sketch the graph of the curve.1.Find the X-intercepts (x,y) and y-intercept (x,y) and the vertical and horizontal asymptotes. 2.Describe the end behavior of the function.Sketch the graph of y=(x^2 +x +3)/x^2, locate all maximum and minimum values, intervals of increase and decrease, and inflection points. HINT: Input your function in to maple. Plot your function using the maple plot command. Find the first and second derivatives of your original functions. Solve the first derivative for x in order to find possible min and max. Be sure to do the second derivative test to confirm min/max by subs critical numbers into the second derivative. Don’t forget to subs these critical numbers into the original function in order to find the co-ordinates of min/max.