1. Find the absolute maximum and minimum on the given interval [1,6]. g(x) = x³ – 6x²

Q: Find the values of constants a, b, and c so that the graph ofy = ax3 + bx2 + cx has a local maximum…

A: Given that: y = ax3 + bx2 + cx has a local maximum at x = 3, local minimum at x = -1, and inflection…

Q: In the function:  f(x)=(12−3x)e^x  What are the critical numbers of the function?  When is the…

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Q: 2. Find the absolute maximum and absolute minimum value of f(x) = 6x – x on [1, 7].

A: Given function fx=6x-x2 To find the absolute maximum and minimum first find critical values.…

Q: f f(x) = ln(x2+10x+16) ov

A: The absolute minimum of f(x) is 6ln(2) and the absolute maximum of f(x) is 4ln(2)

Q: FIND THE MINIMUM AND MAXIMUM VALUE F (X) = X/(1-X) X e(0,1)

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Q: 4. Determine the maximum point of the the graph of y = 12 sin(π – 2x), for x = [-T, T).

A: Given:         y=1-2sinπ-2x     To get the maximum value of the function the derivative is equal…

Q: Find the values of constants a, b, and c such that the graph ofy = (x2 + a) /(bx + c) has a local…

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Q: If functions f, and g are differentiable, and have a maximum distance between the two functions at…

A: Sure. Happy to help.

Q: Find the absolute minimum value of the function g(x) : et x > 0. (7x)

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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: 25 Find the absolute maximum and minimum, if either exists, for f(x) = x+-

A: The second derivative may be used to determine absolute extrema of a function under certain…

Q: 3. Iff has a local maximum at x – 1, then what can you say about f'(1)? What if you also know that f…

A: Given: The function fx has a local maximum at x=1. First derivative test: Let f be differentiable…

Q: Find the absolute maximum and minimum values of ƒ(x) = x2 on[-2, 1].

A: Given,  fx=x2 on −2,1

Q: if f'(x) = x(x-1)(x+3)4 , then f(x) has a local minimum at

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Q: 1 4. Find the maximum value of f (x) = In(x- Inx) on the interval-<x<e. e

A: Given problem:- Find the maximum value of ƒ (x) = ln(x−lnx) on the interval 1/e≤x≤e

Q: 10. At what value of 'x' does a local maximum of y= x^3 - 3x occur?

A: We will solve the following

Q: Find the absolute maximum and absolute minimum of h(x) = x/e^x on [0,4]

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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

Q: #5a) Find the absolute maxımum and abrolute minimum values of f on the given interval. [0,3] X2-X+1…

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Q: Find the absolute minimum of the function f(x)= = 02 GW/N 0.3 4 O 1 0-2 01 2 2x x2 +4 on the…

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Q: Q1- Find any local maximum and local minimum values and sketch the curve: x+ 1 S(x) x² – 1

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Q: Find the absolute extremum within the specified domain. 21) Minimum of f(x)=(x2+4)2/3; [-2,2]

A: According to our policies we are allowed to solve one question at a time. Kindly repost other…

Q: Find constants a and b so that the minimum for the parabola f (x) = x² + ax + b is at the point (4,…

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Q: 5 Find the point X to minimize the function f(x1, x2) =1+¤1 +2x2+ from the strating point X, = using…

A: We are given the following optimization problem : f(x1 , x2) = 1 + x1 + 2x2 + 5/x1 + 10/x2 And we…

Q: 5x f(x) = on the interval[-3,1]. %3| x²+36

A: Given,           fx=5xx2+36 on the interval -3,1

Q: Determine the values of constants a and b so that ƒ(x) = ax2 + bx has an absolute maximum at the…

A: Given:

Q: 2. ts): Find the absolute maximum / minimum values of the function f(x) = x(6-x) over the interval…

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Q: f(x)D has a absolute minimum on [1,3] of 1/319 1/x

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Q: Find the absolute minimum value on (0,∞​) for f(x)=x − 1/x + 14/x^3.

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Q: 1. Identify all the x-values of the candidates for where you might find an absolute maximum or…

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Q: If f (x) = 3 sin x + 7 and g(x) = 2x – 7, what is the maximum value of f(g(x))?

A: Here given that                          f(x)=3sinx+7             and      g(x)=2x-7 We have to find…

Q: 5. The function f (x) = 2kx³ + 3x² + px – 3 has a local minimum at x = -1 and a point of inflection…

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Q: Find the absolute maximum and absolute minimum of  g(t) = t(square root of 4-t) on the interval…

A: Answer

Q: If f'(c) fails to exist and c is in the domain of the function, then: the function has a local…

A: Critical points are the points at which the function is defined, but the derivative is zero or does…

Q: Find out all the relative minimum and maximum values, and sadle points of the function h defined by…

A: Here we have h(x,y)=x3-3x+3xy2 .............................................. (1)

Q: 10. Use the closed interval method to find the absolute maximum and absolute minimum values of f(x)…

A: Maximum minimum value problem....

Q: If f'(x)=x^3-2x^2-x+2, then f has a relative minimum at x=

A: If f'(x)=x3-2x2-x+2, then f has relative minimum at x

Q: 13. Find the minimum and maximum value of the function on the given interval. y = 2x 2 + 4x + 5 [-2,…

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Q: Find the absolute maximum and absolute minimum values of f(x) = 3x^4 +4x^3 −12x^2 +1 on the given…

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Q: What values of a and b make ƒ(x) = x3 + ax2 + bx have a local minimum at x = 4 and a point of…

A: Given: fx=x3+ax2+bx fx has a local minimum at x=4 . fx has a point inflection at x=1 . Since fx…

Q: 1. Find the absolute minimum and maximum values taken by the func- tion f(x, y) = x² + y² – x – y +1…

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Q: 6. For the function y=x³, is x=0 both an inflection point and a local maximum /minimum?

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Q: Find the absolute maximum and minimum values of f(x) = e * – 3x on [0,5].

A: f(x)=ex-3x Take derivative wrt to x f'(x)= ex-3

Q: Consider the function y = 3x - C(In x) where C represents a constant. If this function has a local…

A: If any given function f(x) has local maxima or minima at x=a, then the point corresponding to x=a…

Q: 1. Explain how would you determine the maximum value of y= 1 3-cos x

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Q: 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: Find the critical points that belong to the interval, as well as the absolute minimum and maximum…

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Q: Find the values of constants a, b, and c so that the graph of y = ax + bx + cx has a local maximum…

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Q: 1 Find the absolute maximum and absolute minimum values of f(x) in x² +1 =

A: We are solving the first question and for the next questions post the question againalso mention the…