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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.Use the graph of the function f to find approximations of the given values. The x y-coordinate plane is given. The curve enters the window at approximately x = 0.15 on the positive x-axis, goes up and right becoming less steep, passes through the point (1, 50), passes through the point (2, 75), changes direction at the approximate point (2.47, 77.4), goes down and right becoming more steep, passes through the point (3, 75), passes through the point (4, 62.5), goes down and right becoming less steep, passes through the point (5, 50), changes direction at the approximate point (5.53, 47.6), goes up and right becoming more steep, and exits the window in the first quadrant. (a) f(1) (b) f(2) (c) f(3) (d) f(5) (e) f(3) − f(2) (f) f(3 − 2)Deduction of the second derivative criterion for optimization of functions <br> of two variables using and as related to Taylor
- Functions of the form f(x) = 5 · bkx for k = ±1 will be examined to study the effect of the parameter b on the graph. (a) Graph the function f(x) =5 · 2x. Use the graph to determine the y-values at x-values of −2, −1, 0, 1, and 2. For every increase of 1 in the x-value, the y-value can be found from the previous y-value by ---Select--- the addition of a constant multiplication by a constant . The constant is equal to . (b) Graph the function f(x) = 5 · 0.5x. Use the graph to determine the y-values at x-values of −2, −1, 0, 1, and 2. For every increase of 1 in the x-value, the y-value can be found from the previous y-value by ---Select--- the addition of a constant multiplication by a constant . The constant is equal to . (c) Graph the function f(x) = 5 · 2−x. Use the graph to determine the y-values at x-values of −2, −1, 0, 1, and 2. For every increase of 1 in the x-value, the y-value can be found from the previous y-value by ---Select--- the addition of a…The total cost and the total revenue (in dollars) for the production and sale of x ski jackets are given by C(x)=28x+37,960 and R(x)=200x−0.1x2 for 0≤x≤2000. (A) Find the value of x where the graph of R(x) has a horizontal tangent line. (B) Find the profit function P(x). (C) Find the value of x where the graph of P(x) has a horizontal tangent line. (D) Graph C(x), R(x), and P(x) on the same coordinate system for 0≤x≤2000. Find the break-even points. Find the x-intercepts of the graph of P(x).Please help me found the characteristics of this function in the given image. Please answer these I dont want to re ask them again. The form of the function: The original ordinate is: Number of abscissas originally: The zeros of the function are: Maximum local: Local minimum: When x ->-∞, f(x) ->: When x -> ∞, f(x) ->: Field: Image: The function is increasing when: the function is decreasing when:
- The critical numbers for f(x) = x4 – 8x3 + 16x2 + 5 are x = 0, x = 2, and x = 4. You do not need need to find them. You may also use the fact that the derivative of f(x) is 4x3 - 24x2 + 32x. Find the absolute maximum and absolute minimum on the interval [3, 5].You must use the method from the book and notes; do not attempt to find the answer from a graph.h(x) = 4/((x-1)^2) Show from the definition that the function h(x) = 4/((x-1)^2) is increasing in the interval (-∞, 1) and decreasing in the interval (1,+∞).The graph of a function f is given. The x y-coordinate plane is given. A curve with 3 parts is graphed. The first part is linear, enters the window in the second quadrant, goes down and right, crosses the x-axis at approximately x = −0.33, crosses the y-axis at y = −0.25, and ends at the open point (1, −1). The second part is the point (1, 1). The third part is linear, begins at the open point (1, −1), goes up and right, crosses the x-axis at x = 2, and exits the window in the first quadrant. Determine whether f is continuous on its domain. continuous not continuous If it is not continuous on its domain, say why. lim x→1+ f(x) ≠ lim x→1− f(x), so lim x→1 f(x) does not exist. The function is not defined at x = 1. The graph is continuous on its domain. lim x→1 f(x) = −1 ≠ f(1)
- Derivatives from tangent lines Suppose the line tangent to the graphof f at x = 2 is y = 4x + 1 and suppose the line tangent to thegraph of g at x = 2 has slope 3 and passes through (0, -2). Find anequation of the line tangent to the following curves at x = 2.a. y = f(x) + g(x)b. y = f(x) - 2g(x)c. y = 4f(x)s you walk through Gate 4, you realize that Gate 5 is nowhere to be found. In front of you lies an expansive desert as far as you can see. You look at your map and see that there is an alert for this area. The warning states that this desert is almost entirely quicksand, with only one path safely through the desert. That path is defined by a piecewise function but requires that some parameters be determined before your computer can generate the plot. Thinking back on what you learned in calculus, you realize that your path will need to be continuous. You just need to tell your computer what the parameters below should be in order to create this continuous path. What parameters do you give your computer?Find the critical points and the intervals on which the function f(x)=9x5−3x3+6f(x)=9x5−3x3+6 is increasing or decreasing. Use the First Derivative Test for each critical point to determine whether it is a local minimum or maximum (or neither). (Use symbolic notation and fractions where needed. Give your answer in the form of comma separated list. Enter NULL if there are no critical points.) Open interval(s) where sign of the derivative implies the function is increasing: help (intervals) Open interval(s) where sign of the derivative implies the function is decreasing: help (intervals) Critical point(s) with local minimum: c=c= help (numbers) Critical point(s) with local maximum: c=c= Critical point(s) without a local min or max: c=c=
