Given the function 3x + 6 f(x) = { 32 + 12 z >0

Q: Given the profit function P(x) = 1.3x – 0.01x² – 30, find the value of x at the function's optimum…

A:

Q: Find the particular solution determined by the given condition 314 f'(x) = 3x -6x; f(1) = -6 II

A:

Q: 1) F(x) = Vx+5 %3D x2-16 2x-8 2) h(x) = Vx2-15x+56

A: The domain of a function is the set of values which can be input into a function without the…

Q: 2. Supposef(x) = 5ax³ – 6x² – b²x – 7, and g(x) = cx* + 10x³ – (d + 1)x² – 4x + e. Find values for…

A: The given polynomials are fx=5ax3-6x2-b2x-7 and gx=cx4+10x3-d+1x2-4x+e. We have to find the value of…

Q: 1. f(x) = 2x+5x-3x+4 B(x) = x-2x-1 f(x) +s(x) =

A: 1. f(x) + g(x) = x5 + 2x3 + 3x2 -3x +3   2.  f(x) - g(x) = -x5 +2x3 + 7x2 - 3x +5

Q: Find the particular solution determined by the initial condition. f'(x) = 3x2/3 - 4x3; f(1) = - 8…

A:

Q: Given : f(x) = x² – 3x +1 and g(x) = Vx – 2 g(f(-2)) -

A: Given:     To determine:  g(f(-2))

Q: 3 Given that f(x) = 3x + 7 g(x) = 4x + 5 and h(x) =3x-5 2x 13 find hf(x)

A: Explained below

Q: Find the particular solution determined by the initial condition. 2/3 f'(x) = 3x - 6x; f(1) = - 7…

A:

Q: f(x) = √√√5x - 2, g(x) = x² - 25, and h(x) (fh)(x) = 1 x - 3

A:

Q: Solve f(x) is greater than or equal ro 0 f(x) = x2 + 6x - 7 over x2 -10x + 25

A: We have to solve for the function f(x) when f(x)≥0. Given function -  f(x)= x2 + 6x - 7x2 -10x + 25

Q: A cell phone factory has a cost of production C(x) = 150x + 30,000 and a revenue function R(x) =…

A: Break even point is where total revenue equals total cost. Here total cost is given by…

Q: (c) f(x) = x4 - 1 and g(x) = x4 – x³ – 3x² + 5x – 2 in F(R) -

A: HEre we have to find the GCD of the given polynomIal.

Q: 4. Given the functions h(x) = 3x - 4 find h(x) 5x + 2

A: Here we have to find inverse of function h(x).

Q: 1. Solve for (f1)'(3) if f(x) = x³ + x +1

A: Recall:  d(f-1(a))dx=1f'(b)                ................(1) How to find Derivative of the…

Q: Find the critical numbers of the function. a. f(x) = x³ + 6x2 – 15x

A:

Q: 8. f(x) = 2x +9x + 4 x² -16 a) HA at b) VA at (2x+1)(x+4) (x+4)(x-4)

A: From the given function: fx=2x+1x+4x+4x-4 As we know that for vertical asymptotes , equate…

Q: Given the function f(x) = 1/2x4 – x3 – 2,

A: Given function is fx=12x4-x3-2     .....1

Q: The function f(x) =x³ – 3x2 + 3x -1, x e R has a point of inflection | at A) x = 1 B) x =-1 C) x = 3…

A:

Q: 1. Solve for the values of x in the function below. f(x)=x3-4x-0.5x2+2

A:

Q: 2. Given that f(x) = 2x + 2 and g(x)= find fg 2+x2

A: Given:  fx=2x+2gx=-x2+x2 To Find:  fggfg1=?

Q: Given f(x)=3x¹-8x' +10, find critical points (b) interval increase and decrease

A:

Q: Find f(x) by solving the initial value problem. f'(x)=3x2+4x-3; f(2)=4

A:

Q: 10.Given f(x)=2x-3 and g(x)= x² + 1, solve f[g(x)]

A: We have to find fgx where functions are given as: fx=2x-3 and gx=x2+1. Here we have to find…

Q: If f(x) = x³ – 2.x² +3 , the only point where f could change the concavity is 2 b) x =- 3 a) x =- c)…

A: Finding the inflection points

Q: Find the general solution of the DEs 1- f"(x)= y"(x)=12x +6x-8

A: The given differential equation is a second order differential equation so we will first reduce its…

Q: S(x) = 2x" + 4x + 2x + 1 g(x) = (x + 1) Find (fg)(- 1)

A: Given  f(x) = 2x3+4x2+2x+1 g(x) = (x+1)   We have to find (fg)(-1).

Q: The function f(x) = 2x³ – 21x² + 60x – 7 has two critical values. The smaller one equals and the…

A: The given function is f(x)=2x3-21x2+60x-7

Q: From Variation of parameters for the 2 -1 X' X + e 3 -2

A:

Q: Find f by solving the initial-value problem. f'(x) = 9x² + 6x – 9; f(2) = 5 - f(x) %3D

A: Given,  f'x = 9x2+6x-9  f2 = 5  We have to find  fx

Q: find the critical value of F(x)= 10x^2 + 12x +5

A: The objective is to find critical value of F(x).

Q: The critical points of the function f(x) = 4x³ – 48x +1 are a. 2,– 2} b. d.

A:

Q: The derivative of f(x)= (x2+2x)(x²-2x) is a. 4x3-8 O b. x-4x2 с. none d. 3.

A:

Q: Analyze the critical points of f (x) = x3 − 27x − 20.

A: Critical points of a function at which f'(x)=0 or f(x) is not defined.  f(x)=x3-27x-20 f'(x)=3x2-27…

Q: 2. Let f(x) = 16x 4x and g(x) = 18x + 3. Solve for x when f(x) = g(x)

A: We will solve for x when f(x)=g(x)  in the following step.

Q: The Cost function C(x) and the Revenue function R(x) of a firm are given by C(x) = 4x +1200 and R(x)…

A: Given that the cost function Cx=4x+1200 and the revenue function is Rx=10x. We have to find the…

Q: Find f by solving the initial-value problem. f'(x) = 6x2 + 8x – 9; f(2) = 4 %3!

A:

Q: Find the particular solution determined by the initial condition. f'(x) = 3x273 - 6x; f(1) = - 7…

A:

Q: An animal feed company must produce 200 kg of mixture consisting of ingredients x and x2.x costs 3…

A: we will first formulate the LPP using the given statements and then we will find the optimal…

Q: If f(x) = x2 - 9 & g(x) = 2x - 5 then find the solution for (fog)x) <0

A: We can use the concept of function and inequality in order to solve the given problem.

Q: Find f by solving the initial-value problem. f '(x) =8/(x1/2), f(9) = 51

A:

Q: Find the maximum revenue for the revenue function  R(x) = 372x − 0.7x2.

A: To Determine :- The maximum revenue for the revenue function. Rx = 372x - 0.7x2

Q: 3. For f(x) = x - 10, find the solution to f(x) = 5.

A: f(x) = x - 10 f(x) = 5

Q: Given the profit function P(x) = 1.3x – 0.01x² – 30, find the value of x at the function's optimum…

A: The profit function is: P(x)=1.3x-0.01x2-30

Q: Suppose f(x)=(x−5)(x+4) Solve (x−5)(x+4)=0 for x. What x-value produces a maximum (or minimum)…

A: Given: x-5x+4=0 To Find: Maximum and minimum value of fx. Concept: Suppose that x=c is a critical…

Q: Find the x-values of the stationary points of the function  f(x) = x^4 + 4x^3 - 4x^2 - 24x

A: Given: f(x)=x4+4x3−4x2−24x

Q: 1. f(x) = 3x^3 -2x^2 -4x +1; g(x) = -5x +6x^3 -2 +x^2 . Find (g-f) (x). * %3D -3x^3 -3x^2 + x +3 O…

A: Given: f(x)=3x3-2x2-4x+1g(x)=-5x+6x3-2+x2 To find (f-g)(x)

Q: If f(x) = 4 – x² & g(x) = vx then find (fog)(x) » (gof)( x + 8 If f(x) = 3x – 8 & g(x) = then find…

A:

Q: Find f by solving the initial-value problem. f'(x) = 9x2 + 2x – 4; f(2) = 2 - f(x) %3D

A:

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.