1. An open box is to be made from a 20-inch by 32-inch piece of cardboard by cutting out x-inch by x-inch squares from the four corners and bending up the sides. The largest possible volume of the box is obtained by maximizing V (x) =_ for x in the interval

Q: Find the absolute maximum value of the function y=xV3x-x² on the interval [0, 3].

A:

Q: 7) A rectangle has its two lower corners on the x-axis and its two upper corners on the curve…

A: Follow the procedure given below.

Q: 1. A company manufactures and sells a televisions per month. If the cost and the revenue functions…

A:

Q: Suppose a company wants to introduce a new machine that will produce a marginal annual savings in…

A:

Q: Find the absolute maximum value of p(x)=−x^2−x+1 over [−1,1].

A: Given function is Differentiating with respect to x To find critical numbers of p(x)  That is ,…

Q: Suppose the average costs of a mining operation depend on the number of machines used, and average…

A:

Q: Among the specifications of a company, which requires packing its product in boxes, it is found that…

A:

Q: Find the maxcimum profit and the number of units that must be produced and sold in or der to achieve…

A: Given that, Revenue function: R(x) = x2 + 110 x + 60 Cost function: C(x) = 1.1 x2 + 10 x + 80 We…

Q: Find the absolute minimum and absolute maximum values of fon the given interval. Rx) = x- In(7x), 2…

A: The given function is fx=x-ln7x,  12,2.

Q: 14 Find the absolute maximum and absolute Minimum value of each function: eCx)= 3x"+4x3 interval…

A: Consider the handwritten solution.

Q: If the total cost function (in dollars) of a company that produces x number of portfolios per week…

A:

Q: Find the number in the interval [ – 1, - 0.25] so that the sum of that number and its square is…

A:

Q: Find the positive number x such that the sum of x and its reciprocal is as small as possible. Does…

A: Given the positive number is x

Q: 1. Find the absolute maximum and minimum on the given interval [1,6]. g(x) = x³ – 6x²

A:

Q: A box with an open top is to be constructed from a rectangular piece of cardboard with dimensions 6…

A: Given:       As x is the length of the side of each cut out square, the height of the open-top box…

Q: The absolute minimum value of the function f(x) = 4x² – 8x + 3 over the interval [0, 5] O 1 O 3 o -1…

A:

Q: What is the minimum value of x^2+100/x on a horizontal span of 1 to 5?

A: The given expression is x2+100x;1,2,3,4,5. Let us use the graph to analyze the above function for…

Q: 2. Find the extrema of the function g(x) = x3 using any of the methods given in the above…

A:

Q: Find the critical points of the function f(x) = 8x^3 + 4x^2 - 12x + 10 and determine their nature.

A: Solution: Given: f(x)=8x3+4x2-12x+10

Q: Find the absolute minimum and absolute maximum of f(x)=ln(x2+10x+16) over the interval [0,4]

A: It is given that, f(x)=ln(x2+10x+16)   over the interval 0,4we have to find absolute minimum and…

Q: What is the absolute minimum value of p(x)=2x^2+x+2 over [−1,3]?

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>0. As the width of the…

Q: A box with an open top is to be constructed from a rectangular piece of cardboard with dimensions 12…

A:

Q: 2. Find the minimum value of f(x) = %3D

A: We expert are supposed to do first question . We have to find minimum value

Q: 8. If f(x) = 4 sin x + 6 and g(x) = 3x + 5, what is the maximum value of f(g(x))?

A: Solution is given below

Q: 1. Of all numbers whose sum is 70, find the two that have the maximum product. That is, maximize Q =…

A: Let such two numbers whose sum is 70 and have the maximum product are x and y. So, we have x+y=70…

Q: If f(x) = x3 – 6x² + 9x + 15 then the minimum value of f(x) over the interval [0, 6] is

A:

Q: Suppose that the monthly cost in doliars of mining a certain ore is related to the number of pieces…

A: We have to find the value x

Q: given f(x) = ln(x)/x on the interval [1, 3] What is the maximum value? What is the minimum value?

A:

Q: Find the absolute maximum of p(x)=x2 −x+2 over [0,3].

A: We have to find absolute maximum of f(x) in given interval .F(x) is given as:

Q: 1) Find the Absolute Maximum and Absolute Minimum for f(x) = x³ 9x² +24x on [0,5]

A: At absolute maximum and minimum of a function y=f(x), its first derivative is zero, i.e. f'(x)=0 (a)…

Q: 4. Prove that the interval (0, 1) does not contain a smallest value x.

A:

Q: Find the number in the interval [ – 1, – 0.25] so that the sum of that number and its square is…

A:

Q: Find the absolute minimum value on (0,∞​) for f(x)=x − 1/x + 14/x^3.

A:

Q: 5. The function f (x) = 2kx³ + 3x² + px – 3 has a local minimum at x = -1 and a point of inflection…

A:

Q: If g is a differentiable function that g(x) less than zero for all real numbers x, and if f'(x)=…

A: To analyze the extreme values (if any) of the function f(x) under the given conditions

Q: Find the absolute meximum and absolul-e minimum of fcx) = X intereval [4,8] x- 48X Over the

A: From the given function; fx=x33+x2-48x First, we have to find the critical points; As we know that,…

Q: Find the minimum and maximum of 1 on the interval [0, 3].

A:

Q: The cost, in thousands of dollars, of airing x 30-second television commercials during a major…

A: Hello. Since your question has multiple parts, we will solve first question for you. If you want…

Q: Find the minimum absolute extremum as well as all values of x where it occurs on the specified…

A:

Q: snip

A: Given:                          fx=x+1x Differentiate f(x) with respect to x…

Q: 1. Find two non-negative numbers whose sum is 12 such that their product is an absolute maximum.

A: Let x and y are two non-negative numbers. We have to find maximum of the function Fx,y=xy It is…

Q: A small business determined that the price-demand and cost functions for producing and selling x…

A: Given that, The price demand function is px=70-0.25x and the cost function is Cx=0.5x2+10x+800. We…

Q: Find the absolute maximum and absolute minimum values of f(x) = 3x^4 +4x^3 −12x^2 +1 on the given…

A:

Q: Show that the graph of f(x)=(3-4x)/e^2x has minimum value at x=5/4.

A:

Q: is the total cost of production for a 7-hour day, where x machines are used to produce jackets and y…

A: The Extreme value theorem states that if a function is continuous on a closed interval a, b, then…

Q: The demand for face masks is given by p =-3 In(x) + 10 with domain [1, 28] where x is the number of…

A: Given: The demand for face masks is given by, p=-3 lnx+10, with domain 1, 28 where x is the number…

Q: 6. Find the critical numbers and the open intervals on which the function yx'-3x+2 is increasing or…

A:

Q: 3. Consider the function f(x) = r - 1+x 1- a. Explain why, when evaluated in a floating point…

A:

Q: Find the absolute maximum value of f(x) = x2 - 2x + 6 over the interval 0, 4

A: