Establish the interval where the function h ( x) *x° + 1 is concave down (CD), and find its point of inflection (PI) ||

Q: Find a function f such that f ' (x ) = x 3 and the line x + y =0 is tangent to the graph of f

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Q: Find a first degree approximation of f (x) = In x centered at x = 1.

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

Q: About what point is the local linear approximation l(x): of the function f(x) = tan x valid? 4

A: According to question, Local linear approximation,lx = x2 +π4-12,         .......1Given Function,fx…

Q: -. For the function f, f '(x) =x² -1 and f(4) = -1. What is the approximation of f(3.9) found by…

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Q: Show that the function f(x) = e¯*/2 has inflection points x = f1. at

A: We have the given function as fx=e-x22              ⋯⋯1 As we know that, a point of inflection of…

Q: Find the value of c that makes the function continuous at x = 0. SNIPP

A: Hence it is given that the given function is continuous, so we can write:…

Q: Find the constant a such that the function sin x -13 - S(x) = %3D a+ 11x, x 20 is continuous on the…

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Q: Find Tn centered at x=8 for all n for the function f(x) = ex

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Q: Please

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Q: Given f (x,y) = x³ + y3 – 3y² – 3x² – 9y, find the critical points and use the Second Derivative…

A: solution :-

Q: Assume that f(x) is a differentiable and invertible function so that f(3) = 4 and f'(3) = .…

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Q: Find a function f and a real number a such that :| f(t) dt = x tan-r. + 4

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Q: Find a function f and a real number a such that 4 + | f(t) dt = x tan -1 x. -

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Q: of and dy For the function f(x,y) = In (8x + 9y), find - - of

A: partial derivative of two variable functions

Q: Find the average of the function g (x) = 2 cos 2x on the interval [0, r] -T

A: The function f(x)=2 cos 2x on the interval 0,π

Q: Find a value of x, if any, at which f(x) = Vx – 27 is not continuous.

A: f(x) = (x-27)(1/3) To find :- Value of x where function is discontinuous

Q: Find the local linear approximation L (x)of the function f (x)= x² +3 at x = 1

A: Given that: f(x)=x2+3

Q: Find the linear approximation to f(x) = cos(x) near a =- [Where L(x) = f(a) + f'(a)(x – a) ] 3

A: Solution: The objective is to find the linear approximation

Q: Find the maximum and minimum values of the function f(x) = x – sin x on [0, 27). %3D

A: The given function is: f(x)=x-sinx For maximum and minimum value, differentiate the function and…

Q: Find the linear approximation to the function f(x, y) = sin y --- |T at x, = (1, -2) 2 and use it to…

A: The solution is given as

Q: Find the linearization L(x)of the function at a .

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Q: Find the linearization of the function at a . f(x) = sin x    , a = pie /6

A: The given function fx=sinx, a=π6

Q: Find the linear approximation to f(x)= cot (x) LCx) = f (a) + f'Ca) (x-a). near a=" as

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Q: For f(x, y) = 2y3 + x² – 4x – 4xy – 9, find the critical points and use the - Second derivative test…

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Q: Let f(z) (x-iy)e- ) Determine the points at which exist, and find r(2) at these points.

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Q: Find the linearization L(x) of the function at a. f(x) = sin(x), a 6

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Q: The harmonic function for f(z) = u(x,y) + iv(x,y) to be analytic are:

A: Given that: f=u+iv

Q: Find the absolute extrema of the function on the closed interval.

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Q: Find a function f such that f′(x)=−3x^3 and the line x + y = 0 is tangent to the graph of f.

A: Given: F'(x)=-3x3 and the line x + y = 0 is tangent to the graph of F            We know that…

Q: 3.Find the linear approximation to f(x) = cos x at x, = ÷ and use the linear approximation to…

A: We will use formula for linear approximation.

Q: Find the absolute extrema of the function f(x) = V - x3 on the interval [0, 1

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Q: Find the linear approximation L(x) to y = f(x) near x = a for the function. f(x) L(x) =

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Q: Find the best linear approximation to f on  the interval [-1,1].                        f(x) = x2

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Q: Calculate the approximation of My for the given function and interval f Cx)=フメーンLュ,3 %3D

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Q: Find the values of x where the tangent line is horizontal for f(x) = 3x- 2x-9. %3D O A. x-0, x= ОВ.…

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Q: Apply the first part of the fundamental theorem to determine the value of F'(x) if: e) F (x) = S…

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Q: Find the values of k in f(x)=x^2-kx such that the line y=5x-4 is tangent to the function.

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Q: Let f (x) = sin (2x + 1), 0<x< n. (a) Sketch the curve of y = f (x). ) Find the x-coordinates of the…

A: Given: fx=sin2x+1; x∈0, π

Q: d. Find the linear approximation L(x) for f(x)=x²-x-1 at a = 1.

A: Given function is fx=x3−x−1. d We have to find the linear approximation Lx for function fx at a=1.…

Q: Give the linear approximation of f(x) = x sin(nx2) at x = 2. Use this to estimate f(1.98)

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Q: If f"(c) = 0, then f(x) cannot have a local extremum at x = c.

A: We know, if f"(c) is negative then f(x) have local maximum at x=c and if f"(c) is positive then f(x)…

Q: Let f (x) = 2x* – 3x3 + 5x + 1. Find the value of at x = 1. %3D df-1 - dx

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Q: Find the linearization L(x) of the function at a. f(x)= sin(x), a= π\4

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Q: Use the intermediate value theorem to show that f(x) = (e^−x^2)−x has at least one root in the…

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Q: Use the intermediate value theorem to show that f(x) = e −x 2 − x has at least one root in the…

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Q: Determine the value of k such that f(x) = 4x - kx has a horizontal tangent at x = -1. %3D A 2 В -8 с…

A: Given Data The function is fx=4x2-kx. The horizontal tangent is x=-1.   Differentiate the function…

Q: 3. If f(x) = (1–- t²)e*dt, on what interval is the curve y =f(x) upward? concave

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Q: Find the local extremum of the function • f(x,y) = xy² – 6x² – 3y²

A: Find the local extremum of the function f(x,y) = xy2 - 6x2 - 3y2