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- Consider a differentiable function f with domain R and derivativesf'(x)=-aebx(1+bx) and f"(x)=-abebx(2+bx) , with a and b nonzero real numbers.The function has only one critical point x=-1/b and a local maximum at x=-1/bUse the Second Derivative test to find the value(s) of a and ba. Locate the critical points of ƒ.b. Use the First Derivative Test to locate the local maximum and minimum values.c. Identify the absolute maximum and minimum values of the functionon the given interval (when they exist). ƒ(x) = √x ln x on (0, ∞)Find a linearization at a suitably chosen integer near a at which the given function and its derivative are easy to evaluate. f(x)=6*e-x , a=−0.1 Set the center of the linearization as x=0 The linearization is L(x)equals=_______________
- Use derivatives to find the critical points and inflection points. f(x)=5x - 2lnxEnter the exact answers in increasing order. If there is only one critical point, enter NA in the second area. If there are no inflection points, enter NAf(x)=2x^3+3x^2-12x find the critical numbers of (if any), (b)find the open interval(s) on which the function is increasing ordecreasing, (c) apply the First Derivative Test to identify allrelative extremaFind the absolute extrema of the function on the closed interval. Use a graphing utility to verify your results. (If an answer does not exist, enter DNE.) g(x) = 20(1+ 1/x + 1/x2 ), [−5, 5] Step 1: Begin by finding the derivative of g(x). Step 2: Find the critical numbers and points of discontinuity. (Enter your answers as a comma-separated list.) x = Step 4: Find the absolute extrema. (If an answer does not exist, enter DNE.) absolute maximum (x, y) = absolute minimum (x, y) =
- a. Locate the critical points of ƒ.b. Use the First Derivative Test to locate the local maximum and minimum values.c. Identify the absolute maximum and minimum values of the functionon the given interval (when they exist). ƒ(x) = x2 + 3 on ⌈-3, 2⌉a) f(x) = x2 sin x is restricted to the domain 10 ≥ x ≥ 0 and it has four critical points. They are at x = 0 and x = 2.89 and x= 5.087 and x = 8.096 At what value x in this domain does f(x) attain its maximum? b) What is the minimum value of f(x) = x^2 - 8 ln x on the interval [1,5]4.The derivative of a function f is given by f'(x)=(-2x-2)e^x, and f(0) = 3.A. The function f has a critical point at x = -1. At this point, does f have a relative minimum, a relative maximum, or neither? Justify your answer.B. On what intervals, if any, is the graph of f both increasing and concave down? Explain your reasoning.C. Find the value of f(-1).
- For the function g(x) = 3x2e-x (a) Find all critical numbers. (b) Find the intervals on which g(x) is increasing and on which it is decreasing. (c) Use the first derivative test to find relative extrema.2. f(x) = x^3 − 27x (a) Use the derivative of the function f(x) to find all critical points. (b) Draw and use a graph to classify each critical point of f(x) as a local minimum, local maximum, or neither.a. Locate the critical points of ƒ.b. Use the First Derivative Test to locate the local maximum and minimum values.c. Identify the absolute maximum and minimum values of the functionon the given interval (when they exist). ƒ(x) = -x2 - x + 2 on ⌊-4, 4⌋