If f(z) = (a") + and f(z +y) + f(z-y) Kf(z)f(y), then the 21 value of K.

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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

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Q: Find the values of a and b such that f(x) = x³ + ax² + bx + 5 has x = 1 and x = 2 as critical…

A: The function f(x)=x3+ax2+bx+5 has critical points at x=1 and x=2

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A: The critical number of a function f is a number c such that either f'(c) =0 or f'(c) doesn't exist.

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

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Q: Suppose ff is differentiable on (-\infty,\infty)(−∞,∞), f(3)=12f(3)=12, and f'(3)=-2f′(3)=−2. Use…

A: Given that,  Function f is differentiable on (−∞,∞), f(3)=12, and f'(3)=-2. The linearization of f…

Q: Show that f (−1) = f (1), but that there is no point in (−1, 1) where f (0) is zero. Why does this…

A: Given: fx=1-x2/3 So, f-1=1--12/3=1-1=0 Also, f1=1-12/3=0 Thus, f-1=f1

Q: How can you apply the chain rule in calculus 3 with multivariable calculus

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Q: Find the critical point of f (x, y) = 3x² + xy - 5x + y°, and determine its nature.

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Q: Prove that f(x) = x 2 takes on the value 0.5 in the interval [0, 1].

A: We have to prove that f(x)=x2 takes on the value 0.5 in the interval [0, 1].

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

A: See the answer below

Q: The function f(x) = 2x 30x2 + 126x 1 has two critical numbers. - The smaller one is x = and the…

A: Solution: the objective is to find the critical numbers of the given function

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

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Q: 8. If f(x) = 4 sin x + 6 and g(x) = 3x + 5, what is the maximum value of f(g(x))?

A: Solution is given below

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Q: Find the critical numbers for the function f(x)=|3x-4|.

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Q: Find the maximum value of x if f(x)=5 sin x – Using Quadratic Interpolation with a relative error of…

A: Given: If f(x)=5sin x-x610, find the largest value of x. Using Quadratic Interpolation with a 1%…

Q: The function f(x) = 2x° – 27x² + 108x – 5 has two critical numbers. The smaller one is x = and the…

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Q: f(x, y) 3xy-x² - y²

A: See the details solution in below

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

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Q: 8. Use the fact that the critical points of f(x, y) are found when vf(x,y) = 0 to show that (-3,-2)…

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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 all the critical points of the function f(x) = x^3 - 2x^2 - 15x + 2 on the interval [-1, 3]

A: Let's find.

Q: Find the maximum and minimum value of f (x,y) =x' + 3xy² – 3x² – 3y² +4 = X" - -

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Q: 6 Find the critical numbers of the function f(x) = x5 - * – 12x2 .

A: The given function is  fx=x65-12x12.

Q: 3/ Find the critical numbers of the function f(x)= x/5 (4-x)

A: The given function f(x)=x354-x

Q: The function f(x)=2x^3−27x^2+48x−6 has two critical numbers. The smaller one is x =   and the…

A: The given function is f(x)=2x3-27x2+48x-6                           Differentiate with respect to x,…

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

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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: I'm stuck on this question and I don't know how I should be approaching this. What should I do?

A: To find the critical numbers, first find the derivative of f(x) then set the derivative equal to…

Q: If f(x) = x² + k find k so that f has a critical number at x = 3. %3D

A: To find the critical number for any function fx we have to solve the derivative f'x=0. That is we…

Q: If f:[0, 3] → R is continuous, must its range be a closed interval?

A: If f:[0, 3] → R is continuous, must its range be a closed interval