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Finding critical points Find the critical points of ƒ(x, y) = xy(x - 2)(y + 3).
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- Maximum Sales Growth This is a continuation of Exercise 10. In this exercise, we determine how the sales level that gives the maximum growth rate is related to the limit on sales. Assume, as above, that the constant of proportionality is 0.3, but now suppose that sales grow to a level of 4 thousand dollars in the limit. a. Write an equation that shows the proportionality relation for G. b. On the basis of the equation from part a, make a graph of G as a function of s. c. At what sales level is the growth rate as large as possible? d. Replace the limit of 4 thousand dollars with another number, and find at what sales level the growth rate is as large as possible. What is the relationship between the limit and the sales level that gives the largest growth rate? Does this relationship change if the proportionality constant is changed? e. Use your answers in part d to explain how to determine the limit if we are given sales data showing the sales up to a point where the growth rate begins to decrease.Analyzing critical points Find the critical points of the following functions.Use the Second Derivative Test to determine (if possible) whether each critical point corresponds to a local maximum, a local minimum,or a saddle point. If the Second Derivative Test is inconclusive,determine the behavior of the function at the critical points. ƒ(x, y) = (4x - 1)2 + (2y + 4)2 + 1Analyzing critical points Find the critical points of the following functions.Use the Second Derivative Test to determine (if possible) whether each critical point corresponds to a local maximum, a local minimum,or a saddle point. If the Second Derivative Test is inconclusive,determine the behavior of the function at the critical points. ƒ(x, y) = yex - ey
- Curve tracing. Determine the critical points, points of inflection, and trace the curve.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 intervalAnalyzing critical points Use the Second Derivative Test to classify the critical points of ƒ(x, y) = x2 + 2y2 - 4x + 4y + 6.
- A. State the Second Derivative Test for critical points. B. Find the critical points of the function f(x, y) = x^3 + 3x^2 + 6y^2 − 6xy + 3x − 18y. and use the Second Derivative Test to classify each critical point as a local minimum, local maximum, or saddle point.function: f (x, y) = (2h - y)(y - x^2) a) find all critical points of function b) find the one critical point which is within the cross-section, A (or possibly on the boundary of A) *attached*Analyzing critical points Find the critical points of the following functions.Use the Second Derivative Test to determine (if possible) whether each critical point corresponds to a local maximum, a local minimum,or a saddle point. If the Second Derivative Test is inconclusive,determine the behavior of the function at the critical points.
- Minimum distance Find the point P on the line y = 3x that isclosest to the point (50, 0). What is the least distance between P and (50, 0)?the continuous function has a critical point. (a)Is the critical point a local maximum or a local minimum? (b)Sketch the graph near the critical point. Label the coordinates of the critical point. 1. f(1) = 5, f ′(1) = 0, f ″(1) = −2 2. h(2) = −5, h′(2) = 0, h″(2) = −4Use 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 NA