3. Find the number in the interval E,2] such that the sum of the number and its reciprocal is (a) a minimum and (b) a maximum.

Q: 2- find the absolute max.and min. of the on the closed triangle function P : x* + y Plate bounded by…

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Q: Suppose that f(x, y) = 5x + 2y at which - 4 < x < 4, – 4 < y < 4. %3D Absolute minimum of f(x, y) is…

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Q: Two nonnegative numbers whose product is 25a² (where a 0) and whose sum is a minimum, are

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Q: Please

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Q: 2. On the interval [0,2], determine the absolute maximum, M, and absolute minimum, m. fx) 4x

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Q: Consider two nonnegative numbers x and y such that x + y = 9. Find the x- and y-values that maximize…

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Q: 5. Determine the minimum value of f(x) = e* – 3x on the interval [-1,1] [T:3] %3D

A: Topic:- Maxima minima Minimum value of f(x) is 1.

Q: 85. Find the point on the line y = x that is closest to the point (3, 1). [Hint: Express the…

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Q: Find the absolute minimum value for on the interval [-1,1]

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Q: 9- Find the coordinates of the absolute maximum an d minimum points for f(x)=2x²-x* given x €[0,4] :

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Q: 1. Find two positive numbers whose product is 100 and whose sum is a minimum.

A: Let the numbers are x and y.   It is known that to minimize a function we have to equate the first…

Q: Two nonnegative numbers whose product is 36a? (where a > 0) and whose sum is a minimum, are

A: Now we will solve the problem.

Q: What is the minimum value of x^2+100/x on a horizontal span of 1 to 5?

A: The given expression is x2+100x;1,2,3,4,5. Let us use the graph to analyze the above function for…

Q: A wire of length 10 is to be cut into two pieces, one being bent to form a square and the other to…

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Q: Find the absolute extremd of the on the closed interval. 6x2 g(x) (-2, 1) X - 2 minimum (x, y)…

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Q: ind the maximum of all the possible value

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Q: 13. Of all numbers whose difference is 6, find the two that have the minimum product.

A: Let x and y be such numbers. x-y=6 P=xy. Substitute x=6+y in P=xy and obtain that P=y6+y=6y+y2.

Q: Find the maximum and minimum values of the function f(x, y, z, t) = x + Y + z + t subject to the…

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Q: What is the absolute minimum value of p(x)=2x^2+x+2 over [−1,3]?

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Q: Let A be a positive real number. If the absolute minimum value of f(z) = Ar- 20x on [0, o0) occurs…

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Q: What is the absolute minimum value of g(x)=−2x^2−2x−1 over [−3,4]?

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Q: A ship at point A is 50 yards directly north of point C on shore. Point D, also on the shore and due…

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Q: Let f (x) be the square of the distance from the point (2, 1) to a point (x, 3x + 2) on the line y =…

A: The square of the distance between two points (a, b) and (c, d) = (c - a)2 + (d - b)2

Q: maximum of the quantity xy2 where x and y are

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Q: What is the minimum value of the function f(x, y) on the set D = {(x, y) | 16z² + y² < 1}? = e…

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Q: Prove that if A has n as a minimum then B = {x ∈ R | ∃a ∈ A, x = −3a} has −3n as a maximum

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Q: The sum, of three numbers is constant. Prove that their product is a maximum when they are e v and z…

A: That is to maximize f(x,y,z)=xyz Now, x+y+z=K Let g(x,y,z)=x+y+z-K=0

Q: 2. Suppose that f (a, b) is an absolute maximum of the function f(x, y). Must f (a, b) also be a…

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Q: 2. Find the following: (a) two nonnegative numbers whose sum is 12 such that their product is an…

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Q: What values of a and b make ƒ(x) = x3 + ax2 + bx have a. a local maximum at x = -1 and a local…

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Q: Find the minimum and maximum of 1 on the interval [0, 3].

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Q: Let A be a positive real number. If the absolute minimum value of  f(x)=Ax^5−25x^3 on [0,∞) occurs…

A: A be a positive real number.  absolute minimum value of f(x) where  f(x)=Ax^5−25x^3 on [0,∞) occurs…

Q: Suppose that f(x, y) = x² + y at which 0 < x, y and 3x + 9y < 7. 1. Absolute minimum of f(x, y) is…

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Q: snip

A: Given:                          fx=x+1x Differentiate f(x) with respect to x…

Q: Suppose that f(x, y) = x² – ry + y² – 5x + 5y with x² + y? < 52. 1. Absolute minimum of f(x, y) is…

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Q: 2) Find the absolute minimum value on (0,∞ ) for 4 f(x)= 5+x+

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Q: Suppose that f(x, y) = 5x + 2y at which – 4 < x < 4, – 4 < y < 4. %3! Absolute minimum of f(x, y) is…

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Q: Find two positive numbers that satisfy the glven requirements. The second number Is the redlprocal…

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Q: 20. Find the minimum value of ry+xz+ yz given that r, y, z are real numbers that satisfies the…

A: Note:- As per our guidelines, we can answer the first part of this problem as exactly one is not…

Q: Determine the values of constanas a,b,c, and d so that f(x) = ax^3 +bx^2+cx+d has a local maximum at…

A: Given that f(x) = ax3 +bx2 + cx + d has a local maximum at the point (0,0) and a local minimum at…

Q: 3. Car B is 100 miles directly east of car A and begins moving north at 50 miles per hour. At the…

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Q: (b) Estimate the value of x at whichf has a relative maximum. If there is no relative maximum, enter…

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Q: Find a cubic function f(x)=ax^3-bx^2+cx-d that has a local maximum value of 112 at 1 and a local…

A: Find a cubic function f(x)=ax^3-bx^2+cx-d that has a local maximum value of 112 at 1 and a local…

Q: Suppose that f(x, y) = x² + y² at which 0 < x, y and 5x + 6y < 7. 1. Absolute minimum of f(x, y) is…

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Q: 3. Find the number in the interval ,2] such that the sum of the number and its reciprocal is (a) a…

A: Let number = x,  It is given that, the function is = sum of number and its reciprocal