Boxes are made from rectangular cardboards 6 inches by 14 inches. To form the box, squares are to be cut from the four corners, then the flaps are folded upward. Express the volume of the box as a function of the side of the squares,x.

Q: Determine where the graph of the function F(x) =x²-15x downward. Also, find all inflection points of…

A: We need to determine where the graph of the function f(x)=x3-15x is concave upward and where it is…

Q: Express the function graphed on the axes below as a piecewise function.

A: The graph is,

Q: Express the side length of a square as a function of the length d of the square's diagonal then…

A:

Q: volume

A: Please refer to the image below

Q: Differentiate the function. f(x)  = 3x2 -2cosx

A: Given: f(x) = 3x2 -2cosx Differentiate f(x) with respect to ‘x’

Q: You have 400 feet of fencing to enclose a rectangular lot and divide it in two by another fence that…

A: You have 400 feet of fencing to enclose a rectangular lot and divide it in two by another fence that…

Q: f(x) = 1– 2x +xs

A: Given, function f(x)=1-2x+1/3x^5 By using the formula of differentiation d/dx(x^n)=nx^(n-1)

Q: The perimeter of a rectangle is 422 inches. If the rectangle is x inches long, find a function for…

A: Let us assume a rectangle with length x inches and breadth y inches.

Q: Find the Domain and Range of functions:

A:

Q: Express the area and perimeter of an equilateral triangle as a function of the triangle’s side…

A: Given Side’s length of equilateral triangle is x units.

Q: Determine where the function is concave upward and where it is concave downward. g(x) = 5x^3 = 6x

A: Find double derivative and put it equal to zero to find inflection point.  g'(x) = 15x^2 - 6 g''(x)…

Q: Find the average of the function f (x)= 9x² - óx over [0, 2]. O a. Average = 10 O b. Average = 12 O…

A: Here, we need to find the average of the function f(x) = 9x2 - 6x over [0, 2].  We know that,

Q: You have 600 feet of fencing to enclose a rectangular field. Express the area of the field, A, as a…

A: Consider the dimensions of rectangle be x and y. and Perimeter of rectangle is 600 feet. we know…

Q: f(x) = 3 – 2x +x

A:

Q: You have 800 feet of fencing to enclose a rectangular field. Express the area of the field, A, as a…

A:

Q: A wire of length 8x is bent into the shape of a circle. A. Express the circumference of the circle…

A:

Q: A videoke machine can be rented for P 1000 for 3 days, but the fourth day onwards, an additional…

A: Given:  A videoke machine can be rented for P 1000 for 3 days, but the fourth day onwards, an…

Q: A rectangular piece of cardboard is 4 times as long as it is wide. shorter side is y inches and an…

A:

Q: The hypotenuse of an isosceles right triangle is to be made into a circle C. Express the area A of C…

A:

Q: You have 1000 feet of fencing to enclose a rectangular playground and subdivide it into two smaller…

A: The amount of fencing required would be equal to the sum of length of all the sides including the…

Q: A rain gutter is made from sheets of aluminum that are 20 inches wide. As shown in the figure…

A: Width of aluminium sheet is 20 inches The edges are turned from both sides by x inches. The cross…

Q: A landowner wishes to use 6 miles of fencing to enclose an isosceles triangular region of as large…

A: The isosceles triangular region must have fencing of 6 miles and we must have largest possible area.…

Q: Show whether the function y=x² is considered as even or odd function

A:

Q: Express the side length of a square as a function of the length d of the square's diagonal Then…

A:

Q: H(x) = 3x5 – 4r³ +7 %3D -

A: The given function is: H(x)=3x5-4x3+7 We will use the following formulas:…

Q: Express the perimeter P of a rectangle as a function of the width W if the length of the rectangle…

A: According to the given information:P is defined as the perimeter of the rectangleW be the width of…

Q: Differentiate the function 7) a) f(x) = - 2

A: Here we have to find the derivative of the given function.  Here we use some standard formula of…

Q: A landowner wishes to use 12 miles of fencing to enclose an isosceles triangular region of as large…

A: Let x be the length of the base of the triangle. Fencing is 12 miles. One side base is x . other two…

Q: Find the range of the function for the domain {−2,0,4}. Show your work. f(x)=5x2+4

A:

Q: Determine where the function is concave upward and where it is concave downward. x + 6 x - 6 f(x)…

A: Use the values where the second derivative is zero to set up intervals. Substitute a value into each…

Q: Differentiate the functions. a) f(x) = 1– 2x +*

A: Given problem is  :

Q: A farmer wishes to build a divided pasture adjacent to the river, as shown in the diagram.…

A: Let y be the side of the fence that is parallel to the border of the river side and x be the length…

Q: An open box is to be constructed by cutting out square corners of xx-inch sides from a piece of…

A:

Q: 3* f(x) =

A: Let I denote the open interval (a, b) in R and let x0∈I. Then a function f: I→R is said to be…

Q: From a 12-cm by 12-cm piece of cardboard, square corners are cut out so that the sides can be folded…

A: Please refer the attached image for complete solution.

Q: Differentiate the function   f(x) =    5  - 1 /x

A:

Q: Differentiate the function. 3 F(x) = =* 10 %3D

A:

Q: Express the side length of a square as a function of the length d of the square’s diagonal. Then…

A: Let x be the length of a side, d be the length of the diagonal and A be the area of the square.Now…

Q: Determine where the function is concave upward and where it is concave downward. (Enter your answers…

A: Given function,  f(x)= 3x4 − 18x3 + x − 5 The function f(x) is concave upward on an interval I if…

Q: A function wherein all terms are of the same degree in terms of x and y is known as ________

A:

Q: The revenue from the sale of a product is given by the function R = 5000x-0.1x³ dollars. Use…

A:

Q: Differentiate the function: f(x) = √(1+3e4x)

A:

Q: How does the function f(x)=1/2(x+2)2-3 compare to the parent function? Is it stretched, compressed,…

A: The vertical shift in the graph of y=f(x) is represented by the transformation function: y=f(x)±n.…

Q: Determine where the function is concave upward. ​   ​f(x)x^4-2x^3+7x+5

A: Given: - The function is, f(x)=x4-2x3+7x+5 To determine: - The concave upward of the given function.

Q: Differentiate the function. f(x) = 5x In(8x) – 5x

A: Differentiate the function

Q: An open-top box is made by cutting equal squares of side x out of the corners of a piece of carboard…

A: Given that an open top box is made by cutting equal squares of side x out of the corners of a piece…

Q: Determine where the function is concave upward and where it is concave downward. (Enter your answers…

A: GIVEN

Q: xpressed as a function of x.

A: Given,