e function f(x) = Vx + x7 defined on the [0, 0). Show that v2 < f(x) < /130 on [1, 2] Conclude that /2< / f(x) dx < V130.

Q: f(x) = sin 2x,x e [0,2n]

A:

Q: The function f..) = x+x +3x- 1+2r,x + 2 defined on R has ohly one stationary point. Show that it is…

A:

Q: find the absolute maximum and absolute minimum values of ƒ over the interval. ƒ(x) = (4/x) + ln x2,…

A: Given,

Q: a) Let f(x, y) = x³ + y³ – 3x² – 3y² – 9x. Find and classify all the critical points (whether they…

A:

Q: Find the points of local minimum and  local  maximum of the functions f(x) = sin2x where x belongs…

A:

Q: Find the critical points of f(x) = sin2(x) – cos(x) in the interval (-x, x) and apply the Second…

A:

Q: Find the absolute maximum and minimum values of f(x,Y) = Zx(y-1) + 7 on the region above the line…

A: We have given f(x, y) = 2x(y - 1) + 7. Method of Lagrange Multiplier:  To find the maximum or…

Q: find the extreme values (absolute and local) of thefunction over its natural domain, and where they…

A: The function is given here, For maxima minima, So, the function has only one extrema in its…

Q: function is defined on the closed interval[-4,8] consists of two linear pieces and a semi circle…

A:

Q: The function f(x) = −2x³+3x²+36x has two critical points, c₁ and c₂. Find them and use the second…

A: We need to find and classify critical points.

Q: giver yn f(५) ५) -2x + 3, + 2, find of ax

A:

Q: Since f'(x) > 0 when x 0 (x 1), f is increasing on the intervals (--, -1) and and decreasing on the…

A: Given that: f'(x)=-4x(x+1)2(x-1)2

Q: Find the lineari zation L (x) of the fuction at a. f) = x'+2x

A: In the given question we have to find linearization of function.

Q: b) The critical points for the function f(x, y) = x³ + xy² + 6x² + y² are (-1,3), (–1, –3), (-4, 0)…

A:

Q: 3. f(x) = Vx - 5 is continuous on the interval [5, 0) %3D

A:

Q: A continuous function f satisfies the equation 1 f (x) = x – t+ 2 f(t) dt 0, For all x e [-1, 3].…

A: We have to use leibiniz rule of  differentiating definite integral  d∫f(x)g(x)h(t)…

Q: bounded..by. 3 Find theared of thereyion. R and the line y.=x+2 2. 2. 6%=YG and the line y--x

A: we first find the intersection

Q: Classify the critical points of h(x, y) = x²y + xy² + x²y² + xy³ found in the previous Question by…

A: NOTE: Refresh your page if you can't see any equations. . take the partial derivative with respect…

Q: The function f (x) = x' + 1 is continuous in the interval [-,2, 4] and differentiable in the…

A: Solution-

Q: xsin 1x Vx+1 2tan-x Vx+1 2tan-1x QI) Find of y=: e2x+1

A: We will find dy/dx as following .

Q: Find the critical points of f(x, y) = x³ – 6xy + y³. Use the second derivative test to classify each…

A: For the solution follow the next steps.

Q: 3. Define the function F(x) = S“ sin () dt . For 0 <x < 2, determine: a) %3D The critical points,…

A:

Q: From the partial differential eqiuation by eliminating the arbitrary function z=(x2+y2+z2)

A:

Q: Find the critical point of the function f(x, y) = V 8x2 + 5y2 . Determine whether it is a minimum,…

A:

Q: Find the absolute maximum and absolute minimum values of the function f(x) = 2x – 15 In(7x) on the…

A:

Q: Find the critical point of the function f(x,y)=3e^x−2xe^y. c= Use the Second Derivative Test to…

A: f(x,y)=3ex-2xey First we find critical point from equations fx=0 and fy=0 Then,  Second Derivative…

Q: Find absolute maxima and minima of the function f(x, y) = x² + y² on the closed triangular plate…

A:

Q: find the absolute maximum and absolute minimum values of ƒ over the interval ƒ(x) = x - 2 ln x,…

A: The given function and the interval is,

Q: Find the critical points of the function f(x) = 4 cos² (x) contained in the interval (0, 2). Use a…

A: Follow the procedure given below.

Q: f(x)= X-I x=1 √x-1 X = 1 1123 -s continuous at x = 1?

A:

Q: Find the critical point of the function f(x, y) = 9x 3y- - In(\r+ y|). c = || Use the Second…

A: Let f(x,y) be any function of two independent variables x and y supposed to be continuous for all…

Q: Given function f(x, y) = 1+ xy - x - y. df a) using partial differential involving limits to obtain…

A:

Q: f(x,y) = xln(x^2+y^2)

A: Consider the given function, fx,y=x·lnx2+y2 Obtain the partial derivative w. r. t. 'x' as ,…

Q: Find all critical points of the function y = e(3 e² (3 – x²). Then, using the second derivative…

A:

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: 3z2+x 30. If z – xz – y = 0, prove that- =- ax dy (3z²–x)³*

A: Let's find.

Q: 2x lerivatives from first principle, find the derivatives of y = 5 V3x-e2x-(xln x)(In(In x)) -2e2x)…

A: We have to find the derivative from the given function

Q: (a) Find the critical numbers of the function f(x) = x°(x – 4)5. X = (smallest value) X = X =…

A:

Q: Find the critical point of the function f(x, y) = 24x – 4y² – In(|x + y|). - - c = Use the Second…

A: see below the answer and explanation

Q: 3.) if f(x)= akw f(x) = x-1 and (X) X-1 What is the valule of

A:

Q: Use algebraic methods to determine the critical value(s) of f(x) = x √4−x.  Give your answers in…

A:

Q: Consider a differentiable function f with domain R and derivatives f'(x)=-aebx(1+bx) and…

A:

Q: 4) Let g(x,y) = 2x² + y² – x²y. a. Find the critical point(s) of g. b. Use the second derivative…

A:

Q: Find the critical point of the function f(x, y) = – (25x + 5y² + In(]x + y[). c = Use the Second…

A: As two questions are given, I will solve only one. Given , f(x,y)=-25x+5y2+lnx+y…

Q: Estimate v16.3 using the linearization L(x) of f(x) = /x at a = 16. (Use decimal notation. Give your…

A:

Q: Find and classify all critical points of the function f(x, y) = x + 2y - ln(x4y8) Item 5.pdf

A:

Q: Find the absolute maximum and minimum values of the f(x,y)= x²-2xy+y² function over the D region and…

A: In this question, we have given a function and the region D in figure the function f(x,y) and D are…

Q: f (x, y) = xª – 4.x³ + 2x² + 8xy + 1.

A: To find out the critical points and classify them as relative maximum, minimum or saddle point.

Q: Find the absolute maximum and minimum values of f(x) = (z² + æ)f over the interval [-3, 4]. and it…

A: