2. Determine the maximal interval of existence for each of the following initial value problems: (a) I' = 0.5(r? – 1), x(0) : =1 and (b) r' = x(x – 2), x(0) = 3.

Q: 15) A national distributor of pet toys determines the cost and revenue functions for one of its…

A: The cost function is given by C = 1.2x-0.0001x2 Revenue function is given by R = 3.6x-0.0005x2 To…

Q: 1. The monthly revenue R earned by selling x lamps is R(x)= 120x-0.46x The monthly cost of producing…

A: (a) The given revenue and cost functions are,

Q: 1. An investor invests is a start-up company. The profit in dollars for æ thousand dollars invested…

A:

Q: 10. Given the function f(x) = x³ - 6x2 + 5, %3D RA TOI (a) Find the intervals in which the function…

A: Note: You seem to have posted a question with multiple subparts. We are answering only the first…

Q: 8. Design your own EQUATION for a function f(x) that meets all of the following conditions: f(x) has…

A:

Q: 5. Determine the minimum value of f(x) = e* – 3x on the interval [-1,1] [T:3] %3D

A: Topic:- Maxima minima Minimum value of f(x) is 1.

Q: f"(x) = 13r- (x²-1)a 2.f(x) = f'(x) = r* +1) 4x (x²-1)2 Determine the intercepts. Determine the…

A: f(x) =2x2x2-1Intercepts:x=0, y=0(0, 0),y=0, x=0X and Y-intercept: (0, 0)Asymptotes:x2-1=0x=1, x=-1…

Q: i) Determine the domain of the Following finctions @ f(x) = Sx²+7x+ 2 - Sx°+7x + 2 Oy - log (xt3)…

A: We have to find domain

Q: 18. Given that f(x) =x* – 2x³ +x² + 12x – 7 and f'(x) = x³ – 6x² + 5x + 12 = (x + 1)(x – 3)(x + 4)…

A: To determine the interval on which f(x) is increasing and decreasing.

Q: 11. Find the absolute minimum and maximum of f(x) = r3 - 4x2 - 3x + 3 on the interval [0, 4].…

A:

Q: 1. Employ the following methods to find the maximum of f(x) = 4x – 1.8x² + 1.2x – 0.3x* (a)…

A: Given f(x)=4x-1.8x2+1.2x3-0.3x4. To find: (a) find the maximum using golden search method.…

Q: 4. a. Find the maximum and minimum points for the following. 2 f(x) = 3x3 - 2x b. f(x) = (x² - 9) ³

A:

Q: 1. Match the rule or formula's name with its characteristics by putting the lowercase letter on the…

A: Consider the following

Q: 16. Find the value of the constant k so that the function f(x) = { kx-5 if 0 < x < 2; is continuous.

A: We are given a piecewise function and we need to find out the value of the constant k such that the…

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.