10. Let f(x) = (x² – 4)/(x – 3)³ = (x + 2)(x – 2)/(x – 3)³ %3D |

Q: What is the x-coordinate of the critical point of the function y = (x + 2)^1/3.

A: Given function is y=(x+2)1/3

Q: Two equivalent forms of the Chain Rule for calculating the de-rivative of y = f(g(x)) are presented…

A: Given, if y=fx and u=gx then the derivative of their composition can be expressed as

Q: Minimize f(x) = x² + 54 ; using Interval halving method for 2 ≤ x ≤ 6. E= 10-³

A:

Q: One of the critical points of f(x,y) = x³ – 5y² + 10y – 27x is:

A: The given function is fx,y=x3-5y2+10y-27x. The critical points of a function f(x, y) are obtained by…

Q: 1 max z = 2x, + x2 - x1 + x2 s 1 Xị + x2 s 3 s.t. 2x2 < 4 X1, X2 2 0

A:

Q: 2. Find and classify the critical points of the function f (x, y) = 6x2 – 2x³ + 3y? + 6xy

A: The solution is given below in the next step:

Q: 4. f(x, y) = 10x²y* – 6xy2 + 10x2; fx(x, y), fy(x, y) %3D -

A: Consider the given function as fx,y=10x2y4-6xy2+10x2

Q: If it is known that L {y'' (t)} = -15s+24 with y(0) = -3 and y'(0) = 6, then it can be ensured that:

A: The given problem is to find the Laplace of y(t) from given info, given Laplace of y"(t) =-15s+24…

Q: # 13) Find two positive numbers x and y for which 2x +y = 30 such that xy² is maximized.

A:

Q: 3+2s 17. F(s) %3D (s+4)(s²–3)

A:

Q: Find the critical number(s), c, of the function: f(x) = 3Vx· e-5x

A: Given: fx=3x.e-5x

Q: Max z = x1 + x2 s.t. 2x1 + x2 ≤ 20 x1 +3x2 ≤ 15 x2 ≤ 4 x1, x2 ≥ 0

A:

Q: 15. If g(x) and h(x) are both antiderivatives of some func- tion f(x), then what can you say about…

A: Consider that gx and hx are both antiderivative of function fx. Find gx-hx.   Since gx and hx are…

Q: X, t Xx t 2 Xz531 2X, + X> t Xz Z22 Naximzed By: 233y,tax2tdxg

A:

Q: 1. Find all critical points and investigate the type and stability of each. x' = xy - 2 y' = x - 2y

A:

Q: Differentiate. 11. f(x) = e* %3D 12. (x) = e* 13. g(x) = e2x 14. g(x) = ex 15. f(x) = 6e* 16. /(х)…

A:

Q: (1) If f(x) = { 3 x2 ; -1<x<2, then 0 ; otherwise compute [ xf (x) ]dx and [x²f(x)]dx

A:

Q: What is the particular eq. of the given:   y"-3y'+2y= xe^x +1

A: NOTE: Refresh your page if you can't see any equations. . for the homogeneous system, the auxiliary…

Q: M 10. Integrate f x² ln x dx Oxln x³ + +C Onx-x³ + C Onx²-x³ + C Onx-x³ + C

A: Integrate ∫x2lnxdx=?

Q: What are the critical points of Cobb-Douglas production function  q=K^0.2L^0.6 subject to…

A: First nwe have to change the required equation from 2 variables to a single variable.

Q: 39. Suppose c and d are not both 0, and let ax + b f(x) : cx + d Show that fhas no critical numbers…

A: Please see the explanation below

Q: 15. F(p) 3D (5 р — 2)(3р — 1) 16. g(x) = (/x+ 5x – 2)(Jx – 3/x) %3D 17. y = 7. 18. y = (x - 1)(x –…

A:

Q: I'm studying for a precalculus exam and I want help on this problem because I am stuck.

A: Given that,

Q: Evaluate: √x(x - 5)dx Solution: √ √x(x - 5) dx = f x²(x - 5) dx by law of exponents/ = f (x² - 5x)…

A: Given problem:- ∫√x(x-5) dx

Q: 4Vo Find the critical points of S(x) = x² +

A: Given Sx=x2+4V0x

Q: 1. Find and classify all critical points of the following function: f(x, y) = x* + 2y² – 4ry

A: Given the function

Q: 5 Find the point X to minimize the function f(x1, x2) =1+¤1 +2x2+ from the strating point X, = using…

A: We are given the following optimization problem : f(x1 , x2) = 1 + x1 + 2x2 + 5/x1 + 10/x2 And we…

Q: find the (a) domain and (b) range

A:

Q: The function f(x) = x^3 + bx^2 + c has a critical point at (-2, 6). Determine the value of b and c.

A:

Q: What value of b >-1 maximizes f(b) = J - x) dx!

A:

Q: Suppose the function f(x)=3x^4+ax^3+bx^2 has a critical point at x=2, for which f(2)= −80. Determine…

A: Suppose the function f(x)=3x4+ax3+bx2 has a critical point at x=2, for whichf(2)= −80. Determine a,…

Q: 22) The critical points of the function F(x,y) = x³ + 3xy + y3

A:

Q: 6) Find most general antiderivative of the fxn. a) f(6) = x5+2x²-1 X' B) 4(1) - 2 +30*

A:

Q: 7. The function (x, y)= (2x* + y* )exp + xy' is homogenous in x and y of degree

A: .Given,f(x,y) = (2x4+y4) ey2x +x y3Put y= xSo we get,f(x,x)= (2x4+x4) ex2x +x x3 f(x,x)= (3x4) e0.5…

Q: Suppose that the function f(x, y) = x°y+ax – 8y + 5 has a critical point at (2, –2). What must the…

A: For a function of two variables, f(x, y), a critical point is defined to be a point at which both of…

Q: 9 2. If fS(x)dx= 37 and g(x)dx=16, = 16, find [2f(x)+3g(x) ]dx- %3D 0.

A:

Q: 1) If h(x) = x³ +1, find h-'(x). (A) h-'(x) = 3+ (x +2)³ (B) h-(x) = Vx – 1 (C) h-(x) = 2r³ – 3 (D)…

A:

Q: (1) In(x - y) = xy + y³ ;

A: According to rules, I need to solve first question.. Please repost remaining questions

Q: 15.)What is/are the critical value(s) or point(s) of the function h(x) =x³ +x² + x? %3D A. x = -1 C.…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 1. Find and classify the critical points of f (x, y) = 6xy – 4x³ – 3y?

A: Critical points of f will occur: fx and fy is o. Given equation is f(x,y) = 6xy-4x3-3y2…

Q: Show mathematically that MRS is increasing for U=1-ex +e2y and is diminishing for U=lnX +LnY

A:

Q: In x +1 If y = then will be 2x³ – 3x' (2x³ – 3x) G+1) – (In x + 1)(6x² – 3) (2x — 3х)? А. (2x3 — 3х)…

A: SOLUTION-

Q: Find the critical points of the function f(x,y)=x^2+y^2+6x−10y+1

A:

Q: dy Ify드a2-4x-의. then. dx x2 2x-2) 2-4x-5 einz2-4x-5)- In(z+2)]. x2-4x-5 x2 x2-4x-5 x 2 x 2 2-4x-5…

A: Consider the given equation:

Q: In Exercises 7–10, determine from its graph if the function is one-to-one.

A: Since we only answer up to three sub parts. We’ll answer the first three. Please resubmit the…

Q: let 2.+ (3(x-1+4y+!j". ニ ): find the Critical points f f.

A: In the question we have to find critical points.

Q: minimize F=x^2+y^2 subject to xy^2=16.

A: Let F=x2+y2 and G=xy2-16=0...(1) Let λ be the Lagrange's multiplier. Then Fx=λGx and Fy=λGy⇒2x=λy2…

Q: 1 Given f(x)=³-57² +24r, which of the critical number found in the previous number is f(c) a…

A: You must have an idea about to how to find relative maximum or minimum using critical points.