Please solve this question using application of derivatives!!   A conical tank is designed so that the sum of the radius and the height of the cone is 60 inches. Find the radius and height of the tank of maximum volume. What is the exact maximum volume under these conditions?

Q: find the derivative using increment method show complete solution thanks, i'll like back y=x^(3)…

A: To find the derivative of y=x3-x-2 using the increment method. Note that the derivative using…

Q: 7. уз y =/x³ – 1/1+ vx

A:

Q: Find the solution of the equation y= 2x -x- 10 in the interval (2, 4] using derivatives. You can use…

A: To solve an equation  f(x)=0 using derivative of function, we can use the formula…

Q: 3x+4 3. f(x) = x2+3

A:

Q: Find the derivative of ƒ (x) = /7– 8x. %3D To enter va, type sqrt(a). f' (2) =

A: We have to find the derivative of the given function.

Q: the equation ariables x and y and

A:

Q: Find the derivative of the function by the limit process. f(x) = x2 - 2 %3D f'(x) = 2x %3D Need…

A: Apply Limit rule

Q: Find the approximate volume of a spherical shell whose linear radius is 3 inches and whose thickness…

A: Find your answer below

Q: Show that y=sec^2x and y=tan^2x have the same derivative. What can you say about y=sec^2x-cot^2x?

A: Given y=sec²x and y=tan²x Now derivative dy/dx=d/dx( sec²x) =d/dx(1+tan²x) dy/dx= 2tanx sec²x   Now…

Q: y Arctar 3-V9-x2

A: Given: y=tan−1x3−9−x2 To find: the second derivative of the function

Q: How is derivatives utilized in solving for the dimensions and total area of a box?

A: Here we to write how is derivatives utilized in solving for the dimensions and total area of a box.

Q: 1. f(x)= Vx3 + 2x² + 3 2. f(x) = (6x – 7)(2x + 3)

A: To find the second derivatives of the given functions.

Q: y = In (x+2), (х-1)2

A: Given that: y=lnx3x+2x-12

Q: y у %3 4a/сosh a

A: Consider the given hyperbolic function y=4acosha The given function can be written as, y=4acosha=4a…

Q: Is this calculus statement true or false: "We can determine that h(x) =x^4 has a minimum at x= 0…

A: Given function is  Then x=0 is critical point of h as h'(0)=0, but also h''(0) =0  Therefore,…

Q: 4. y=ysin 2xcos 5x + 3

A: Find your answer below

Q: 3x+4 3. f(x) = x2+3 12 x3+6x2+3x 4. f(x) = 3x

A:

Q: Compute the derivative using derivative rules that have been introduced so far. y = (8x4 + 5)3

A:

Q: By using the definition of derivatives, find f'(2) for f(x) = Vr +7. You may not get any credit if…

A:

Q: Find the derivative of the functron. Simplify and express the answer anly. using positive expenents…

A: In this question the given function is y=(x2-5)3x2+3 we have to find y' In positive exponents only

Q: Find the derivative by the limit process. f(x) = 10 – x2 %3D

A: We know that the derivative of a function fx is given by:f'x=limh→0fx+h-fxh

Q: (f°9)(x) if f(x)=2x3 +1 and g(x)=6x +5

A: We have to find the composition of the function then have to find the second order derivative.

Q: Solve for the derivative of t y =2 V3-z Previous

A: This is a basic differentiation problem

Q: Find two positive numbers whose product is 750 and for which the sum of one and 10 times the other…

A:

Q: rconh(3x+1) - 5t +ldt f(x)= sinh³

A:

Q: Use the limit definition of the derivative to find the instantaneous rate of change of f(x) = 2x² +…

A: We will find the instantaneous rate of change of f(x) at x=4 as following.

Q: Acrsin a2_v2

A:

Q: Please show me the partial derivatives for this homogenous equation and solve for GS/PS using Test…

A: Exact differential equation

Q: 6. Use the definition of derivative to find f'(x) if f(x) 3D х2 — Зх — 4

A:

Q: y= 3x³etan ( – 4x)

A: Topic:-  derivatives

Q: Find the derivative of the function by the limit process. f(x) = 7x – 6 %3D

A: The derivative is calculated using the limit process as follows. f'x=limh→0fx+h-fxh Now, fx+h=7x+h-6

Q: We want to use the Richardson method to calculate the first order derivative antisymmetrically at…

A: We need atleast 2 points to calculate the Richardson second order derivative. The small parameter…

Q: Find the equation of tangent line to the curve y = 2 - x 2 (7, ²/7). at the point (7, Express the…

A: The objective is to find the equation of tangent line.

Q: A piece of wire, 370 cm long, is to be bent into an isosceles triangle. What should the exact…

A: given: A piece of wire, 370 cm long, is bent into an isosceles triangle. we have to determine what…

Q: Choose the correct value of derivative. d dx x+1 X () is equal to (Hint: Look at the note of section…

A:

Q: Vx-3 6. f(x) = X-9

A:

Q: 1. f(x)= Vx3 + 2x² + 3

A: topic - second order derivatives

Q: ential equation is given by

A:

Q: f(x)%3D (6- x²)3 — х? %3D

A: DIFFERENTIATION OR DERIVATIVE The differentiation is a process of finding the rate of change of one…

Q: f(x) = (6x – 7)(2x + 3) %3D

A: Given  f(x)=(6x-7)(2x+3)

Q: What information can be obtained from derivatives? Please provide 2 examples from the real world and…

A:

Q: A company has identified that the revenue R for a particular product is given by the equation R(x)…

A: The given Revenue function R(x)=23x3-40x2-450x.  Task: To maximize this revenue function.

Q: 3. х %3D у* — 2у3 2y3

A: We can find the answer as below using delta method

Q: Find the derivative by the limit process. F(x) = 13 -

A:

Q: Describe how you would use the second derivative to determine a local minimum or maximum.

A: Given data is: How you would use the second derivative to determine a local minimum or maximum

Q: Solve for the derivative of the function using chain rule. 6. f(x)= cot(6x3+5)

A: Derivative

Q: Find the partial derivative. Find fx(3, -7) when f(x,y) = 7x2-9xy. O -21 O -126 O 21 O 105

A: differrntiate partially with respect to x

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.