(7) Does the extreme value theorem tell us that f (x) = ! has an absolute maximum and absolt minimum on the interval [-1,1]? Why or why not? Be specific.

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: Given the function f(x) = (x+3)²(x-1). Find the critical points of f(x) and its increasing and…

A: f(x)=x+32x-1f'x=x+32ddxx-1+x-1ddxx+32       =x+32+2x-1x+3       =x+3x+3+2x-1      =x+33x+1to find…

Q: Find the x-coordinates of all critical points of the given function. Determine whether each critical…

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Q: Find thecritical points of the . function f(xy) and indicate with evidence whether they are local…

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Q: On the graph of f(x) = cos x and the interval [27, 47), for what value of x does f(x) achieve a…

A: Here given function

Q: Does g(x) = e^x - x have an absolute minimum value? An absolute maximum? If so, find them or give…

A: Find the critical point

Q: 5. If c is a critical point of F(x), when the is a local maximum or minimum at c? Explain

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Q: Find the x-coordinates of all critical points of the given function. Determine whether each critical…

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Q: Find the absulote maximum of x40-x20 on the interval [0,1],also find its absolute maximum value

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Q: Find the absolute minimum maximum if they exist for f(x) = x+ 4/x

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

A: In algebra, an equation can be defined as a mathematical statement consisting of an equal symbol…

Q: At what x-value is the global minimum for f(x)=x2−4x+3 within the interval  0≤x≤5?

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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: Does x=6 belong to a local maximum or a local minimum? Does x=0 belong to a local maximum or a local…

A: Here we have,  differentiate with respect to x

Q: Determine whether the following statement is true or false, and explain why. The secant function has…

A: Given: Statement: The secant function has an infinite number of critical points where an absolute…

Q: Find the absolute maximum and absolute minimumvalues of f on the given interval.   f(x) =12 +4x  -…

A: We find the critical points by solving f'(x)=0

Q: Does ƒ(x) = (7 + x)(11 - 3x)^(1/3) have an absolute minimum value? An absolute maximum? If so, find…

A: Check the function has absolute minimum value.

Q: Consider the following function f(x)=2(x+1)2 in the interval [-2, 3] The critical point(s) =…

A: For critical points put f'(x)=0.

Q: The function ƒ(x) = |x| has an absolute minimum value at x = 0 even though ƒ is not differen-tiable…

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Q: If an even function ƒ(x) has a local maximum value at x = c, can anything be said about the value of…

A: A function is called even function if f(-x)=f(x)Even function is symmetric about the y axis.

Q: 4. If f has a local minimum at x = 0 and a local maximum at x – 2, what can you say about f'(0) and…

A: f has a local minimum at x=0 and a local maximum at x=2.

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

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Q: Is it true that a discontinuous function cannot have both an abso-lute maximum and an absolute…

A: It is known that if f is continuous on a closed interval [a, b], then f has both absolute maximum…

Q: Find the absolute minimum value of f() = xe on [-5,0].

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Q: Find the minimum and maximum values of f(x) = on the interval [6,7] by comparing values at the…

A: We will see that function retains its sign in the given interval and in decreasing function. hence…

Q: Let a > 0 and f(x) = x + . Then ƒ has An absolute maximum at x = -Vā A local minimum at x = Vā A…

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Q: В f has a relative maximum at x = 1. f has neither a relative minimum nor a relative maximum at x =…

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Q: Q2: Find all critical numbers of the function f(x) = (x- 2)2/3 +1 and classify each critical point…

A: Here we will find out the required value.

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: Find the absolute minimum value on (0,infinity) for f(x)=4e^x/x^2

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Q: If f has a local minimum at x = 0 and a local maximum at x = 2, what can you say about f'(0) and…

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Q: Find the x-coordinates of all critical points of the given function. Determine whether each critical…

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Q: What is f(x) = x +1/x absolute maximum and absolute minimum at the range [0.2, 4]

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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…

A: Find first derivative.

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: at 2 Find absOIute maximum & minimum value fu)=x²-1 on [lile)

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Q: Calculate the difference d between the global maximum and global minimum values of f(x)=x2−4x+6 in…

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Q: 4. Find the absolute minimum and absolute maximum values of on the interval 1,2

A: The function is given by,

Q: Find the absolute minimum value of the function f(x) = et (0, 0). on

A: Given function f(x) = exx    on   0 , ∞

Q: Consider f(x) = 1/x on [1,∞). Find all the critical points. Is there a maximum? If yes, find it. If…

A: here, objective is to find  the critical points of the function f(x)=1/x on [1,8)

Q: If f(x) has a relative minimum value at x = 4, then f'(4) = 0 or f'(x) is undefined at x = 4 Select…

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

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

Q: Find the x-coordinates of all critical points of the given function. Determine whether each critical…

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Q: ind the x-coordinates of all critical points of the given function. Determine whether each critical…

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Q: Where are there local minimum(s)/maximum(s) f(x)=3(2x-1) -4(x+1)?

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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: 3 The absolute minimum value of f(x)=x³ on the closed interval [-1,8] is a) 0 b) -1 c) 1 2 d) -…

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Q: What is the x-coordinate of the global minimum of the function f(x) = x – 3 ln x – 2 for the…

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Q: 3] If the critical point of the function f (x,y) = 10 xye-(x²+y') is (,). test this point %3D…

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