The hourly operating cost of a plane which seats up to 405 passengers is estimated to be $5,214. If an airline charges each passenger a fare of $110 per hour of flight, find the hourly profit P it earns operating the plane as a function of the number of passengers x. [HINT: The cost function is constant (variable cost = 0).] P(x) = Specify the domain. (Enter your answer using interval notation.) What is the least number of passengers the plane must carry to make a profit? (Round your answer up to the nearest whole number.) passengers

Q: The absolute minimum value of the function f(x) = 9x² – 18x + 8 over the interval [0, 10] O 1 O 8 -1…

A: Find the minimum value of the given function.

Q: The average cost per hour in dollars of producing x riding lawn mowers is given by the following.…

A: We have to find - the number of riding lawn mowers to produce in order to minimize average cost,…

Q: The absolute maximum of the function f(x) = 2x² + 4x + 16 over [1, 6].

A:

Q: The function f(x)=12-6x4 has an absolute maximum value of _____________ and this occurs at x equals…

A: Given, Function f(x)=12-6x4

Q: Suppose that the selling price p of an item for the quantity x sold is given by the function 1 x +…

A: To find the maximum revenue and items to be sold to obtain maximum revenue.

Q: Find the minimum point for the function f(x) = 5x – 14x2 – 11x + 1

A:

Q: find a so that f (x) = ax2 + 8x -8 has a minimum value of -24

A: According to the given information, it is required to find the value of a so, that the function f(x)…

Q: The absolute minimum value of the function f(x) = 4x2 – 8x + 8 over the interval [0, 5] O 4 O 5 O 6…

A: To find absolute max/min we have to find local max/min in a given interval and also function value…

Q: The absolute minimum value of the function f(x) = [0, 5] 4x² – 8x + 8 over the interval 8 9. 4 11

A:

Q: The area of a parallelogram bounded by the y-axis, the line x=6, the line f(x) =6+2x, and the line…

A: The line parallel to y = 2x +6 will be of the form y = 2x + k…

Q: The absolute maximum of the function f(x) = 3x2 + 3x + 14 over [1, 7].

A: We first find the critical points using the f'(x)=0 f(x)=3x2+3x+14f'(x)=6x+30=6x+36x=-3x=-36x=-0.5

Q: The profit function for good x is given by P(q) = 200 + 1009 + 30q²-9² where q is the quantity of x…

A: It is provided that the profit function is P(q)=200+100q+30q2-13q3. We need to determine the maximum…

Q: For what value of x does the function f(x) =x³ 4x attain the absolute minimum %3D in the interval…

A:

Q: The function f(x) = x8 + 4x3 –- 7x + 13 has where the absolute minimum occurs, correct to

A: Given, the function        f(x)=x8+4x3-7x+13

Q: A small island is 2 miles from the nearest point P on the straight shoreline of a large lake. If a…

A: GivenLet x be the distance point PSmall island is 2 miles from the nearest point PWoman on the…

Q: Please

A:

Q: Find the minimum value of the function. f(x) = -2 - 2x + x2

A:

Q: Find the location of the indicated absolute extremum for the function. Minimum 4 4 3 -1 -2- X = -3 Ó…

A:

Q: The absolute minimum value of the function f(x) = 6x² – 12x + 7 over the interval [0, 7] O 8 O 8 O 1…

A:

Q: Find the absolute extrema of the function on the closed interval. f(x) = x³ – 12x, [0,6] minimum (х,…

A:

Q: The absolute minimum value of the function f(x) = 9x² – 18x + 3 over the interval [0, 10] 6. -6 3 4

A: The absolute minimum value of the function f(x)=9x2-18x+3 over the interval [0,10]

Q: The absolute minimum value of the function f(x) = 7x² – 14x + 9 over the interval [0, 8] 10 O 14 O 9…

A: For absolute maximum and minimum we need to check value of f(x) on critical points and boundary…

Q: Let f(x)=-x +6x-8, 0Sx <6.. What is the minimum value of f(x) (Write a number only)?

A:

Q: Find the intervals of convexity and concavity of the function f(x)=−x3+6x2−2x+1.

A: f(x)=−x3+6x2−2x+1 f'(x) = -3x2 + 12x - 2 f''(x) = -6x + 12

Q: Find the maximum and minimum values of the function Z = 8X1 + 5X2, subject to the following: 3X1 –…

A:

Q: Find the location of the maximum absolute extremum for the function. O A. x=5 A (x) 6- B. x=3 O C.…

A:

Q: An open box is to be made from a 20-inch by 32-inch piece of cardboard by cutting out x-inch by…

A: As we are making a box, its height must be greater than 0. So we have x&gt;0. As the width of the…

Q: Find the minimum value of the function f(x) = 2x² + 18.3x + 45 to the nearest hundredth.

A: Given function f(x)=2x2+18.3x+45

Q: Find the absolute maximum and absolute minimum values, if any, of f (x) = x³ + 3x² + 1 on the…

A: Absolute maximum point is a point where the function obtains its greatest possible value. Absolute…

Q: Find the critical points and determine whether they are minima, maxima, or neither: f (x) = x2/3(1 −…

A: Given: fx=x231-x

Q: Find the absolute maximum value of y = x³-3x2 + 2 in the interval [-1,3]. (-1,-2) (0,2) O (1,0)…

A:

Q: Find the intervals of convexity and concavity of the function f(x)=2x3−18x2.

A: We find the second derivative of f(x) using the power rule.

Q: A tractor has a first cost of $40,000 and a salvage value of $15,000 in year 10. The MARR is 12% per…

A: Option B

Q: Let p=24−x and ​C(x)=329+5​x, where x is the number of garden hoses that can be sold at a price of​…

A: (a) Consider the given information. The profit function and the cost function is px=24−x and…

Q: A piece of cardboard measuring 9 inches by 12 inches is formed into an open-top box by cutting…

A: Given:- A piece of cardboard measuring 9 inches by 12 inches is formed into an open-top box by…

Q: The absolute minimum value of the function f(x) = 4x? – 8x + 8 over the interval [0, 5] 11 9. 4 16…

A:

Q: Find the consumer and producer surpluses by using the demand and supply functions, where p is the…

A: We will equate the demand and supply function to find number of units at equilibrium.

Q: The absolute maximum of the function f(x) = 3x² + 3x + 12 over [1, 6].

A: f(x)=3x2+3x+12    over  1,6firstly, we have to find critical pointsf'(x)=6x+3=0⇒6x=-3   ⇒x=-36=-12

Q: For what value of x does the function f(x) = -x3 – 4x attain the absolute minimum in the…

A: The value of function which is least in entire range of function is called minimum value of…

Q: What is the minimum of the function y = -x° + 3x for x <-1? -4 O-2 4. O 2

A:

Q: Find the global and global minimum of the function f(x)=x4−8x2+3 within the interval [−1,2].

A:

Q: Please

A: The given function is

Q: for what value of x does the function f(x) =1/3x3-4x attain the absolute minimum in the interval…

A:

Q: Which function has a greater minimum? f(x) = 5(x – 4) - 3 6. 5 4- y = g(x) 3+ 十+ -7-6-5 4-3-2 1 234…

A:

Q: A clothing company determines that its marginal​ cost, in dollars per​ dress, is given by the…

A:

Q: Find the mascimum or minimum value of the function. F(x) = 2x² + 8x - 1

A:

Q: Find the global extrema of the function f(x)=3x4−6x2+2 on the interval [−2,2]

A: Global extrema of a function exists at critical points or at the end points of the interval.…

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.