x + 2, х < 2 f(x) | /2r, x 2 2 ||

Q: Let ​h(x)=​f(g(x)), where f and g are differentiable on their domains. If ​g(−1​)=2 and g′​(−1​)=7​,…

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Q: Consider f(x) = xe−kx for k &gt; 0. Find the relative extrema and the points of inflection of the…

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Q: f(z) is a twice differentiable function with f(0) = 1, f(2) = 4, f'(2) = 5, Then af"(x)dx = %3D

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Q: 3 Let f(x) = 2 + In(bx), where b is a positive constant. Find f'(x).

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Q: let                    x^2+1   if x is less than 1 f(x)=                   x+1        if x is…

A: Consider the given function fx=x2+1  if x&lt;1x+1   if x≥1. The point is x = 1. Obtain the left hand…

Q: f(x) = 4x^3-(x+9)^1/2 What is the interval or intervals on which the function is differentiable on…

A: Refer  to the question the provided function is f(x) = 4x^3-(x+9)^1/2.

Q: 1) Find the absolute extremum values of f(x) = x? [1, 2]. 2x +24 over the interval %3D -

A: Topic - maxima minima

Q: 3. Consider the function f(2, y) = x° + 7a? + 2æy + y? – 19r – 4y + 1. Find all critical points of f…

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Q: Determine if the MVT applies to the function on the given interval. If so, find the points that are…

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Q: The function f(x) = e + e has a relative extremum at Select one:

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Q: Determine if g(x) is differentiable at x = 0 if g(x) = { cube root 1-4x3, x ≥ 0 sech…

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Q: Dicuss the contiunity of the function f (x,y) = ln  (x+y-1)

A: We know: 1) Polynomials are continuous everywhere. That is, at every point in real number 2) Sum of…

Q: f(T) is a twice differentiable function with f(0) = 5, f(1) = 4, f'(1) = 2, Then Calo

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Q: 2) An elastic tire is described by the iven by the function f(x, y) = 4xy. Use

A: Introduction: The Lagrange methodology is employed to maximize or minimize a general performance…

Q: determine if the piecewise-defined function is differentiable at the origin.

A: Consider the given function fx=2x-1,                x≥0x2+2x+7,         x&lt;0 The left hand and…

Q: At which r-values is the following function g differentiable? Explain and compute, where necessary.…

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Q: Find the absolute maximum and absolute minimum values of f on the given interval: f(x)= square root…

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Q: Let be a real function of y=f(x) real variable implicitly defined by the equation 2xy−x2y2+ey=0.…

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Q: 1 For a function f(x), we have f(x) = 1+ x? and f(0) = 0 prove that x +y f(x) +f(y) =f 1-xy

A: We will prove as following.

Q: Differentiate the following functions 1. f(x) = In(tanh²(x³ + 2x + 1)) 2. y = csch?(3x) 3. y = x³…

A: There are some functions are given , we have to find its derivative function.

Q: Find given that z is a differentiable function of x and y, and xz + yz3 = 2 +x²ev

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Q: Find the absolute extrema of the function on the closed interval.                      h(t) = t/(t +…

A: Given: The function h(t)=tt+3 and the interval [-1, 6].

Q: Find the absolute maximum for the function f(x) = re, x E [-1,3] %3D

A: Given :       function  f(x) = 12x2e-x       Interval  x∈ [-1, 3]    To find : Absolute maximum…

Q: 4). If f(1) = 12 and f' is continuous and | f'(x) dx=17, what is the value of f(4)?

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Q: Let f be a differentiable function such that f(-1) = 10 and f' (x) = x – 2. What is the…

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Q: Let = (x – 3)(x – 1)2 for a differentiable function f which is defined on the interval [0,4]. %3D dx

A: TO FIND THE CRITICAL POINTS, INTERVALS OF INCREASE AND DECREASE VALUE OF 'X' AT WHICH LOCAL EXTREMA…

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: Calculate the derivative of the following functions

A: Given: y=fx gx5 To determine: Derivative of the given function

Q: 3. Find the absolute extrema of the function f(x) = vx - x on the interval [0, 1]. %3D

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

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Q: Show that the function is differentiable at x=0 and find f'(0). f(x) = x2sin(1/x), if x is not…

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Q: A function y = f(x) is continuous and differentiable on the interval (0, 7). If f(x) dx = 13, f(1) =…

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Q: if x 0 f' _(0) f',(0) Is f differentiable at 0? Yes No

A: To find f is differentiable at 0 or not

Q: 4). If f(1) = 12 and f' is continuous and f'(x) dx=17, what is the value of f(4)?

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Q: If f(x) is a twice differentiable function with •1 f(0) = 5, f(1) = 4, f'(1) = 2, Then So 2x f"…

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Q: 25. Use the definition of differentiability to prove that the following function is differentiable…

A: First let us find the partial derivatives of the given function f(x,y)=x+y as shown below:…

Q: 11.2.4. f(x, y) = V]xy|.

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Q: Find f'_(0) and f'„(0) for the given function f. (If an answer does not exist, enter DNE.) if x 0…

A: Hey, since there are multiple questions posted, we will answer the first question. If you want any…

Q: (c) Does there necessarily exist a differentiable function h with 0 < h(x) <1 and E = {x : h(x) = 0}…

A: Sol:in the given question we have to tell about the differentiable function f(x)s.t whose range is…

Q: f(x) is a twice differentiable function with f(0) = 4, ƒ(1) = 3, f'(1) = 6, Then So 3xf" (x)dx =

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Q: find the length of the function over the given interval x=2y, y=-1, to y=1

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Q: Find the linear approximation L(x) of the function f(x) = (1-x)1/2 at a=0 and then use L(x) to…

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Q: 3. Find constants A and B such that the function x2 f(x) = if x 2 is differentiable at x = 2.

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Q: f(x,y) = x [(In x)2 + y2] %3D find the extreme points of the function

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Q: H.W Ex 2: Determine if the f(x) is continuous at x = 3 ? [x² – 1 f(x)=- |x² + 2 at x=3 at x+3

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Q: Find a good numerical approximation to F(4) for the function with the properties that F'(x) = e-x+15…

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

A: Given:   f(x) = sin x,       on  56, 116Since…