Solve the following problem min f(x1, x2, x3) subject to x1x2x3 xi + x2 + x3 = 1 ||

Q: d the local max and min values of the function f(x)= 3x3 – 2x if it exists.

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Q: Let Ax) = x³ + 9x² – 6x + 2. Find f (x) and f"(x), and then solve f"(x) = 0.

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Q: If f(1) =1 and f (x) 2 3 for 1 <x < 3, how small can (3) possibly be?

A: We will find the smallest possible value of f(3) as following.

Q: Find the particular solution determined by the given condition 314 f'(x) = 3x -6x; f(1) = -6 II

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Q: Suppose z is implicitly given as a function of x and y, according to The equation: y−zx3=1−yz2 The…

A: Suppose z is implicitly given as a function of x and y, according to The equation: y−zx3=1−yz2 The…

Q: On which interval(s) is the function f(x)=(12/5)x5-3x4-8x3+5 increasing?

A: Given function is,

Q: 1. if f(x)= x2-4,  g(x)=x3 , F(x)=1/(x-3) a. F(g(y)) b. f(square root of x4+2)

A: F(g(y)) can be obtained by replacing x by g(y) in F(x)

Q: Let m & n be constants and suppose f(x) = {" + 3bx + 2x² , x 1' тx + b What are the values of m and…

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Q: 13 Given that f(x)= 2x+1 and h(x)=x, find (h o f)(3).

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Q: -3х - 4 х-1

A: Increasing interval : Interval in which graph goes upwards Decreasing interval: Interval in which…

Q: Find the particular solution determined by the initial condition. f'(x) = 3x2/3 - 4x3; f(1) = - 8…

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Q: Consider the following problem; max f (x, ,x2) = xỉx2 subject to 2x + x = 3

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Q: If f(2) = 15 and f (x) > 2 for 2 s x s 4, how small can f(4) possibly be?

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Q: 1. Solve for (f1)'(3) if f(x) = x³ + x +1

A: Recall:  d(f-1(a))dx=1f'(b)                ................(1) How to find Derivative of the…

Q: If f(z) = 5.7x +6.9, then, f(x+h) is:

A: Given : fx =  5.7x+6.9

Q: Given the function P(x) = (x – 1)²(x – 4) - -

A:

Q: If f (x) = x²cos-(x² – 4), what is f'(x)? 2x3 o f'(x) = 2xcos-'(x² – 4) – V 1-(x²-4)² 2x3 o f'(x) =…

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Q: 2. If f (2) = 10 and f' (x) = x²f (x) for all x, find f"(2).

A:

Q: Consider the following problem; max f (x1 , x2) = xỉ x2 subject to 2x} + x = 3

A: The given function is, max f(x1,x2)=x12x2 subject to 2x12+x22=3So, f=x12x2 and let g=2x12+x22-3

Q: Given that f(x) = 3x – 1, g(x) = 2x and h(x) = x + 1, determine: a. hgf(x)  b. hgf(-2

A: Given : f(x) = 3x-1             g(x) = 2x             h(x) = x+1  To Find : hgf(x)…

Q: If you need to prove that a ∈ f^−1 (Y ), what do you need to show?

A: Here we need to show the way to prove a∈f-1(Y)

Q: If f(x) = 2x² + 4x - 3, then f(x+h)-f(x) h 012x+ +2h)²+(4x+4h)−3−(2x²+4x-3) h 2(x+h)² +4x−3−2x² -…

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Q: (x -1, if 0 < x < 1 2x f(x) = |x – 3| , g(x) = -4 Vx, h(x) = %3D , if

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Q: ? Suppose that * f(3) = 1, and f(x) > 0, and f(x) < 0. Is it possible that f(2) = 3 4

A: Given fι 3=12  and    fιx&gt;0and fιιx&lt;0 . it is possible that fι2=34let g3 =  fι 3=12    ,…

Q: -1, if -n <x<0 1, if 0sxSa h) f(x) = { %, -1<x<0 0<x<1 -x, if %3D if

A: We find Fourier coefficients then find required Fourier series.

Q: Let k(x)=f(x)g(x)h(x). If f(x)=−2x−3,g(x)=−3x+3, and h(x)=−3x2+x+1, what is k′(1)?

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Q: The critical numbers of the function f(x) = x³ – 6x2 are x = 0 and x = -4. Select one: True O False

A: Given; fx=x3-6x2   As we know that; To calculate the critical numbers of the function, f'x=0.   And…

Q: Graph the following functions.

A: The function: fx=-2x-1if x&lt;-11if -1≤x≤12x-1if x&gt;1

Q: Find f by solving the initial-value problem. f'(x) = 9x² + 6x – 9; f(2) = 5 - f(x) %3D

A: Given,  f'x = 9x2+6x-9  f2 = 5  We have to find  fx

Q: Consider the following problem; max f(x₁, x₂) = -x²-x² subject to (₁-1)³ ≥ x² Check whether the…

A: As per the question we are given an optimization problem with objective function : f(x1 , x2) = -x1²…

Q: Analyze the critical points of f (x) = x3 − 27x − 20.

A: Critical points of a function at which f'(x)=0 or f(x) is not defined.  f(x)=x3-27x-20 f'(x)=3x2-27…

Q: 2. Let f(x) = 16x 4x and g(x) = 18x + 3. Solve for x when f(x) = g(x)

A: We will solve for x when f(x)=g(x)  in the following step.

Q: Show that the function f(x)=x3−3x2+6x−1 is strictly increasing on R.

A: Let us find f'(x) using the power rule

Q: (b), f(x) = In (x² – 4)

A: Since you are asking only for b. Here is your answer.

Q: Discrete

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Q: What are the critical points for the function f(x) = x³ + 9x² + 15x – 8 %3D None x = -1 and x = -5 x…

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Q: Consider the following problem; max F(x1 ,X2) = x,x3 subject to 6x + 3x3 = 72

A: Solution is given below:

Q: Find the critical numbers of the function f (x) = 2x3 + x? + 2x

A: Given:            f(x)=2x3+x2+2x

Q: If f(x) = 3x – 2 and g(x) = x + 1, then (f(g))-'() equals O 1– x O x +1 O x – 1 1 O (3x – 1) 3

A:

Q: In Problems 21–32, use Descartes’ Rule of Signs to determine how many positive and how many negative…

A: Use Descartes’ Rule of Signs to determine how many positive and how many negative zeros each…

Q: Find the value of (A+ V)²(x² + x) with h=1.

A: To find the value of Δ+∇2x2+x with h=1.

Q: Find the critical points of f(x) = abs(10x-1)

A: Given function is                                         f(x)=|(10x-1)|…

Q: Find a number c that satisfies the conclusion for f(x) = x + x-1 on the interval [0, 2]

A: Answer is 2/√3

Q: Consider the following problem; max f(x1 ,x2) = -xỉ – x} subject to (x1 – 1)³ > x3 b. Find the…

A: We need to find solution.

Q: Let f(x) = - 8(x – 1)(x + 9)(x – 8)(x – 7). Solve: (a) f(x) > 0 (b) f(x) < 0

A: The given function is fx=-8x-1x+9x-8x-7. (a) Substitute fx=-8x-1x+9x-8x-7 in fx&gt;0:…

Q: Suppose that 2 sf (x) < 4 for all values of x. What are the minimum and maximum possible values of…

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Q: SOLVE FOR THE X OF THE FOLLOWING FUNCTION USING REGULA FALSI a. 4x² + 3x3 = 0

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Q: If (2)-3.f(2)-1, g(x)=1/x, and htx)-[fx)][g(x)], then what is h'(2)?

A: Given that h(x)=[f(x)][g(x)] So, using the product rule,  h'(x)= [f'(x)][g(x)] + [f(x)][g'(x)] Then…

Q: Find the particular solution determined by the given condition. f'(x) = x2/5 + x; f(1) = -6 f(x) = =…

A: We can find the particular solution as below.

Riemann Sum

Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence this method makes it simple. Usually, we take the help of different integration methods for this purpose. This is one of the major parts of integral calculus. 

Riemann Integral

Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.