S f(x) = x² – 2x + 6 x > 1 x4 + 2.x3 + 2 x <1 Show that there c E (-2,3) such that f(c) = 4. (Don't Find c).

Q: - (4y" + fy) = -A with y(-1) = -2, y(-1) = 1, y"(-1) = 0 Use x1 = y, x2 = y', and x3 = y". x + with…

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Q: (1) A course repeater claims that his brother who did some Calculus at college years ago, but…

A: Given: fx=2x−1x2+3x2+1, and gx=x2+872−3x25 To check whether: f'x=4x2x2−1+2xx2+3−2xx2+12x2−1x2+3x2+1,…

Q: The value of (x,f(x)) for the upper and lower limits of the function fx=x^3-6x^2+4x+8 and for the…

A: Given function is fx=x3-6x2+4x+8find the upper and lower limits of the function for the period…

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

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Q: Minimize f(x) = x² + 54 ; using Interval halving method for 2 ≤ x ≤ 6. E= 10-³

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Q: The function f(x) = 2x 36x + 210x – 4 has two critical numbers. The smaller one is x = and the…

A: Thw critical points are given below

Q: 1.If f(x,y) cos(4x-2y)+ln(y² -2x) find £xy fx fxy,

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Q: The function f(x) = 2a – 392? + 240x – 4 has two critical numbers. The smaller one is x = and the…

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Q: The function f(x) = 2x – 42x + 270x – 2 has two critical nu The smaller one is x = and the larger…

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Q: # 13) Find two positive numbers x and y for which 2x +y = 30 such that xy² is maximized.

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Q: If fCx) is bdd Junchion an f(x) dx = の-3 then 3. True or Fal se ?

A: Solution :- An odd function is defined such that f(−x)=−f(x)

Q: The function f(x)=2x^3−36x^2+162x−9 has two critical numbers. The smaller one is x = and the…

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Q: 1. Find the roots of the given equation where f(x) = 0 with the stopping criterion of 0.001. f(x) =…

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Q: 1. If f(x, y)=3x' cos y– y sin x– 2.x In y- yln x-4x²y, find ôf ôf d²ƒ _ô²ƒ

A: According to question given thatf(x,y)=3x3 cosy-y2 sinx-2x ln(y)-y ln(x)-4x2y

Q: The function f(x) 2x – 33x2 + 108x – 1 has two critical numbers. The smaller one is x = and the…

A: Explained below

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: Let f(x) 18xe 18 %3D (a) f'(x) : (b) Solve f'(x) 0 to determine the critical values of f.

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Q: 27The platis that passes through the e Point C672) and contains the lihie メー4-2t)X= 345t) Zと+4t 4. こ

A: We have to find the equation of the plane which passes through the given point and contains the…

Q: 1 Find f(1) if f(t) dt = x" - x + 2x? – 2, x >1.

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Q: Please show steps.

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Q: Find the critical numbers of the function: f (x) = e²–9z

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Q: of of and ду Find f(x,y) = Vx + 3y?

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Q: Find the critical numbers of the function.…

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Q: 6) If y=x² +1+ f dt , prove that y"= 2 - x2

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

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Q: The function f(x) = 2x° 39x + 240x – 11 has two critical numbers. The smaller one is x = and the…

A: Topic = Derivative

Q: If f (x) = x(x - 2), then the critical points %3D of the function f(x) are

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Q: 3. Find the fixed point(s) of f: [1, ∞)→→ [2, ∞) defined by f(x) = √²+x.

A: 3) To find: fixed points of f:[1,∞)→[2,∞) defined as f(x)=x2+x.

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: - The antiderivative of f (x) =; whose graph passes through the point (C 3+5sinx+. +3cosx 1(. 5 1(.…

A: Introduction :

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: -5z Calculate F" (2) if F (x) = |(1- t)dt. %3D +1 O F' (2) = 5 (1– 252?) O F' (x) = 1- 24a? %3D O F…

A: We will use the formula Where

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: Let f(x) = 18xe - 1s. (a) f'(x) (b) Solve f'(x) = 0 to determine the critical values of f.

A: Recall: (uv)'=u'v+v'u

Q: 19 Suppose that Ts Cx) centered at 2 for f (x) is gicn by Ts Ca):345Ca-2)+5 Cx-2)?ょ2x-2)+(x-2) Than,…

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Q: what is the antiderivative F(x) 0f f(x)=3x^((1)/(2))-x-1that satisfies the condition F(4)=0 A,…

A: Given that:f(x)=3x1/2-x-1, F(4)=0

Q: Find the critical numbers of the function of f(x) = (x^3)/3 −16x

A: Given function is : fx=x33-16x To find the critical number of point.

Q: (1) A course repeater claims that his brother who did some Calculus at college years ago, but…

A: We use the quotient rule, product rule, and chain rule of differentiation to check the claim of the…

Q: 2. Find all critical numbers for the function: g(x) = x/2x +1 B. 0. ÷.글 1 1 А. - - | 2 3 2 c. - D.…

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Q: Find the critical numbers of the function. x – 1 | f(x) : x² + 4

A: The quotient rule of differentiation states that: d dxuv=vdudx-udvdxv2. At critical points of a…

Q: Consider the following function: f(r) = 2r + 3z² – 12z Find the critical numbers of f. (x = ?)

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Q: 1. f(x) = Vx - 1 at x = 5 %3D 2. f (x) = at x = 2 x-2

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Q: The value of Wronskian of two functions y, =7* and y2 =7** is

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Q: Find ý of the function x2 - e2x+3y - In(xy) = 0. %3D

A: Consider x2-e2x+3y-ln(xy3)=0We differentiate it implicity, we…

Q: (1) A course repeater claims that his brother who did some Calculus at college years ago, but…

A: Using the product rule of natural logarithm, it can be written that ln(ab)=ln(a)+ln(b) . Using the…

Q: Find constants c1 and c2 such that F(x) = c1xe -x + c2e -x is an antiderivative of f(x) = 3xe -x .

A: Given: Fx=C1xe-x+C2e-x  and fx=3xe-x

Q: Find constants a and b in the function f(x) = axb such that f(-) = 1 and the function has a In(x)…

A: Given that the function is  f(x) = abx/ln(x) such that f(1/2) = 1 and the function has a local…

Q: 25 p1 3) Compute f(x)f'(x) dx where f(x) =x +2, using the Composite Trapezoidal 2 rule, your results…

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Q: find thr critical numbers of the function f(x)=1/3x^3-4x^2+12x+2

A: Consider the function

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…