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First Derivative Test
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- How are the absolute maximum and minimum similar to and different from the local extrema?Find the critical points and test for Maxima/Minima. Show your complete solution.4) Determine the critical points of the functions below and classify them as relative maximum, minimum or saddle point. write on paper
- 4) Use the level curves in the figure to predict the location of the critical points of f and whether f has a saddle point or a local maximum or minimum at each critical point. Explain your reasoning. Then use the Second Derivatives Test to confirm your predictions.locate all relative extremum and saddle point (if any) ofSHOW COMPLETE SOLUTION Find the critical point of y=xex
- The critical point is a: -saddle point -maximum -minimum ?Based on the image attached, a) Identify the critical points of the function.b) Determine the intervals on which the function increases and decreases.c) Classify the critical points as relative maximums or relative minimums.Find absolute maximum and minimum points, if they exist, of f(x)=x^3+x^2-X+1 on the interval [-2,1/2]. Need to show work to find all critical points in the interval
- Find the x coordinates of all critical points of the given function. Determine whether each critical point is 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)=2x^3-6x+7 x=____(smaller value) x=____(larger value) Find any critical numbers for ƒ and then use the second derivative test to decide whether the critical numbers lead to relative maxima or relative minima. If ƒ″ (c) = 0 or ƒ″ (c) does not exist for a critical number c, then the second derivative test gives no information. In this case, use the first derivative test instead ƒ(x) = 3x3 - 3x2 + 1Does ƒ(x) = 2ex/(1 + x2) have an absolute minimum value? An absolute maximum? If so, find them or give reasons why they fail to exist. List all critical points of ƒ.