f(x) = x² – 10 on [-2, 3]

Q: Suppose (1,1) is a critical point of a function f with continuous second derivatives and fz = 44,…

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Q: Find f-1 if f (z) = iz + 1.

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Q: = x2 - 4x + 1 with domain [0, 3] f has ---Select--- v at (x, y) = f has ---Select--- v at (x, y) = f…

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

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Q: The function f(x) = 2x 30x + 126x – 6 has two critical numbers. %3D The smaller one is x = and the…

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Q: Analyze the critical points of f (x) = (2x − x2)ex .

A: fx=2x-x2ex Differentiating with respect to x, we get…

Q: of f(x, y, tion of ve

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Q: Show that the linearization of ƒ(x) = (1 + x)k at x = 0 is L(x) = 1 + kx.

A: The given function is

Q: Find aa and bb so that the function f(x)={4x^3-3x^2+5, x<-2         {ax+b,             x is…

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Q: Let f(x, y) = 3x² – x – 3y + 5y2 – 10xy. - - - List the critical point:

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Q: Find all critical points of the function f(x) = x4 – x-

A: Critical point is 5/4 Explanation is given below

Q: If f(x) = etan-¹(x²-3) then f'(x) at x = 2 is equal to

A: SOLUTION-

Q: 2. Use the Mean Value Theorem to show that f(x) = 2x sinh(x - 1) + 2* -x has a critical number…

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Q: The function f(x)=2x^3−33x^2+108x-4 has two critical numbers. The smaller one is x =?    and the…

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Q: Is ƒ(x, y) = x2 - xy + y2 - 3 more sensitive to changes in x or to changes in y when it is near the…

A: Partial derivative of f w.r.t a variable is the indicator of the sensitivity of f towards that…

Q: #! Find f'cx) if fex)= Čx²+SX+2)(X-)

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Q: Find all critical points of the function f(x) = 2 – 2x + 2. %3D

A: topic - derivatives

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

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Q: (9-x) ₁/x = (x

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Q: 2. Use the Mean Value Theorem to show that f(x) = 2x sinh(x - 1) + 2* – x has a critical number…

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Q: 2. Use the Mean Value Theorem to show that f(x) = 2x sinh(x – 1) + 2" – x has a critical number…

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

A: The given function,  fx=5x ln x

Q: State why the function 2z2 - 3z + e-z is analytic everywhere.

A: See the answer below

Q: Show that the function f : [0, 1] →[0, 1] given by f(x) = (x −1)2 has a fixed point. Can you apply…

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Q: Find the absolute maximum value of f(x) = x2 – 2x + 10 over the interval 0, 3 -

A: Find your answer below

Q: Find all the critical numbers for the function g(x) = % xª -- x3 - 5x?

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Q: Find all FIRST and SECOND order critical POINTS for f(x) = (x² +x – 2)'/3

A: fx = x2+x-213f'x = 13x2+x-213-1 . ddxx2+x-2        = ddxx2+ddxx+ddx-23x2+x-223        =…

Q: Differentiate the function f (x) = 4 cos 3x - 3 sin 4x. %3D O -4sin 3x -3cos 4x O -12(sin 3x + cos…

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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: Find the critical numbers of the function.   f(x)  = 4 +1/3x  - 1/2x2

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Q: Determine f such that f′′(x) = 12x − 1 and 1 is both a critical number and a y- intercept of f

A: Given:  and 1 is both critical number and y-intercept.

Q: 4.x +1 1 with f'(x) = 1/ 56x2 - 156x + 115 14x – 19 - - 3. Let f(r) = and f"(x) 4 %3D 3 5 Vr2 – 3x +…

A: To find the points on which it is concave up or concave down

Q: 6. Determine f such that f"(x) = 12x – 1 and 1 is both a critical number and a y- intercept of f.

A: A differential equation is an equation in x,y and derivatives of y. A linear differential equation…

Q: Suppose that f(x, y) = yVx³ + 1 on the domain D = {(x, y) | 0 < y <x < 3]

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Q: Find the critical numbers of the function  f(x) = 4x - tan x

A: fx=4x-tanx Differentiating with respect to x, we get f'x=41-sec2x=4-sec2x

Q: The function f(x) = 2x 33x + 168r - 1 has two critical numbers. - The smaller one is x = and the…

A: In this question we are given with function x and we have to find the critical points of the…

Q: Q1) check the continuity of fX) at X--1, 0,1.2,3 -1<x<1 f(x) = 2x-1, 3x-2 2SxS3 2, 1=3

A: As per the answering guidelines we need to answer only first question so please repost the other…

Q: Find all points c satisfying the conditions of the MVT for the function f(x)=x3−x in the interval…

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

A: Let's find.

Q: 13,4) f(x.y) =In(x + x² +y² If Find x

A: f(x,y) = ln (x+x2+y2)∂f∂x=∂ ln (x+x2+y2)∂x=1 (x+x2+y2)×(1+12x2+y2)×2x

Q: Classify the critical point (5,-4) for f(x,y) = x² + 4xy + 2y2 + 6x-4y +3

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

A: Given,          The function kx=x2lnx2

Q: The coordinates of the critical point according to the criterion of the first derivative of the…

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Q: Find all the critical points of f(x) = 4x³ – 3x. %3D V3 z = V3 x = 0

A: The given function f(x)=4x3-3x

Q: Compute f(c+h)−f(c) at the indicated point. f(x)=6x2​; c=4

A: Given : Function : f(x) = 6x2   To find : f(c+h)−f(c) at c = 4.

Q: If F(X) is an antiderivative of *-2 + x-', then what is the value of F(1) - F(-1)?

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Q: Find the linearization of ƒ(x) = 2x at x = 0. Then round its coefficients to two decimal places.

A: Given function is,

Q: defines 2 as y. y- cos (3x2) = 5 a function of x and • differentiate implicity to find az ду

A: