10) Decompose the function h(x)=2x–10 into a composition of two functions f(x) and g(x) such that (gof)(x)=h(x)..

Q: EXERCISE 1. Find equation 2. For the E different- Xフ5 -h (x 5oɔ 9-T)(XUIS h+ X) =(x) J () a) f(x) =…

A:

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: 7. Find all the critical points of f(x) = (x² – 4x – 4) e² %3D and classify them.

A:

Q: Find the critical numbers of the function.    g(x)=x^4-2x^2+3

A: The given function is g(x)=x4-2x2+3.

Q: f f(x) = ln(x2+10x+16) ov

A: The absolute minimum of f(x) is 6ln(2) and the absolute maximum of f(x) is 4ln(2)

Q: 22. The function f(x) = Vx – 6 is transformed according to (x, y) → (7x – 7, - y+1). the transformed…

A: Substitute fx for y in the transformation and simplify. x,y=x,f(x)→7x-7,-f(x)+1=7x-7,-x-6+1

Q: Let g be a function that is defined for all x, x # 2, such that g(3) = 4 and the derivative of g is…

A: Critical points of the function are the point either the derivative is not defined or derivative is…

Q: x*y"-xy'+y = 0 Y, = In x

A:

Q: Find all the critical points and local maximums and minimums of each function. f(x) = 5x+cos(2x+1)

A:

Q: Find the critical numbers of the function.…

A: Critical numbers of a function are the numbers for which first derivative is zero or undefined. Now…

Q: 7. Find the absolute maximum and absolute minimum values of f(z) = 2x – 3r2/3 on the interval…

A:

Q: (a) Prove and verify that the gradient of the tangent line to the curve f(x) = V5x² + 3x – 1 at…

A: Given curve f(x)=5x2+3x-1differentiate…

Q: Find the absolute maximum and absolute minimum values of f on the given interval. f(x) = ln(x2 + 5x…

A: The given function f(x) = ln(x2 + 5x + 13),    [−3, 1] Differentiate with respect to x…

Q: 5. Find the linearization, L (x) f (a) + f' (a) (x – . a) of the given function "f" at "a". %3D - f…

A:

Q: The function f(x)=2x^3−36x^2+162x−9 has two critical numbers. The smaller one is x = and the…

A:

Q: 7. Find the critical numbers of the function. (1) ƒ (x)= x³ + r² – r

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: Suppose that a consumer derives his utility from two goods, the amounts of which are x and y,…

A:

Q: x*y"-xy'+y = 0 c) Y, = In x

A: Let's find.

Q: 2. Find the extrema of the function g(x) = x3 using any of the methods given in the above…

A:

Q: Find the critical numbers of the function. f(x) = 5x In x %3D X =

A: The given function,  fx=5x ln x

Q: 4. Consider the logistic map f(x) = (1+ v6)x(1 – x) • Find the fixed point of 2-periodic cycle. •…

A:

Q: (1) A course repeater claims that his brother who did some Calculus at college years ago, but…

A: for f'(x) see 2nd and 3rd step. for g'(x) see 4th and 5th step.

Q: (a) Show whether if 0<x <1, f(x) = 2 - x if 1<x < 2 is a Dirichlet function.

A:

Q: Find the linearization L(x) of y = e5* In(x) at a = 1. L(x) =

A: Given that:y=e5xln(x)a=1To find the linearization

Q: Determine all critical points for the function. f(x) = x3 - 12x + 3 x = -2 and x = 2 Ox = -2 O x = 2…

A:

Q: Let f(x)=(7+3x)4   f(x) has one critical value at A =

A:

Q: In the function:  f(x)= (3x^2)ln(x) , x&gt;0 What are the x-coordinates of all local minima and…

A: Given:f(x)= (3x^2)ln(x) , x&gt;0

Q: 2. Give an example of a regulated function f on [0, 1] such that f(x) > 0 for all æ e (0, 1), So…

A:

Q: Determine the GINI Index of Country X whose Lorenz curve is f(x) =;x² +÷x*. If Country Z 3 has a…

A: The Lorenz curve  of country X is f(x)=12x2+12x4. The GINI index  of a certain country with Lorenz…

Q: ,2 Let f(x) = x – 12x -27x + 1. Find the critical points of f(x).

A: Find the derivative as follows: f'x=ddxx3-12x2-27x+1        =3x2-24x-27

Q: Find and classify all critical points of the function f(x, y) = x+2y-In(x¹3³)

A: Given :f(x,y)=x+2y4-lnx4y8

Q: for the funciton f(x) = x^3 - 75x Its local maximum  is____, which occurs at _____> Its local…

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: 1. Consider function f(x,y) for which = 24x² + 114y and %= 114x + 24y2. Wbich of the points (5, 5)…

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

Q: Let f(x) = (2 – x)° f(x) has one critical value at A = | 0

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: Find all critical numbers of the function g(x) = x^4 - 10x^2

A: Using definition of critical numbers.

Q: Find the absolute maximum and minimum vaules of the funct ion g(x)= (x^2-3x+4)/(x-1) on the interval…

A:

Q: 26 a. The function f(x)=x- 6x² + 9x-3 is defined on the interval [0,5]. Find the critical points of…

A: Since you have asked multiple questions in single request so we  will be answering only first…

Q: Find T; (x): Taylor polynomial of degree 5 of the function f(x) = cos(x) at a = 0. T3(x) = %3D

A: f(x)=cos x at a=0, we have to find Taylor polynomial of degree 5.

Q: 8) State the critical points of the function k(x) = x2 In x2.

A: Given,          The function kx=x2lnx2

Q: Find the critical number(s) of the .4 * (function f(x)=In(2x)/(3x )2 نقطة( In(2x) f (x) 3x e/2 and 0…

A: Calculus

Q: Let g(x)=x3-6x2-15x+20. Find all critical points for this function

A:

Q: 3. Find the critical numbers of the function g(x)= 5x -8.

A: Given:

Q: 1 2. (a) Express f(x) = into partial fractions. %3D (x2 + 1)(x – 1)2² Hence, evaluate f(x)dx.

A: As per Bartleby instructions only one question can be solved. Upload others separately.

Q: 16-17. Find the derivative: y = (x2 – 4x + 2)(2x3 – x2 + 4) A) 2x*- 36x³ + 24x2 + 4x -1 B) 2x* –…

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Q: y = In[(2x – 1)(x + 3)] with Respect to x by using the chain rule.

A: