Suppose that 2 sf (x) < 4 for all values of x. What are the minimum and maximum possible values of f(5) – f(3)?

Q: Find the absolute maximum and absolute minimum 3 of f(x) = + x² – 35x over the interval [3, 7]. 3

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Q: find a so that f (x) = ax2 + 8x -8 has a minimum value of -24

A: According to the given information, it is required to find the value of a so, that the function f(x)…

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: Find the absolute maximum and absolute minimum of the function f(x)= x² – 4x + 3 over [1, 4].

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Q: Consider the function f(x) = 4 – 5x", – 3 < x < 2. - - The absolute maximum value is and this occurs…

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Q: The function x2 f(x) = 1 - x has a local maximum when x = 2. Select one:

A: We will check if the given statement is correct.

Q: Find the absolute maximum value of p(x)=−x^2−x+1 over [−1,1].

A: Given function is Differentiating with respect to x To find critical numbers of p(x)  That is ,…

Q: Find the absolute maximum and absolute minimum values of f(x) = r3 – 9x2 + 24x – 3 on [2,5]. -

A: Given:- f(x) = x3 -9x2 +24x-3  To find:- Absolute maximum and minimum of f(x) in [2, 5]

Q: Consider the function f(x) = 3 – 5x², – 5 < x < 1. - - The absolute maximum value is and this occurs…

A:

Q: If f(x) = x – kx-1 has a relative maximum at x = -2, then the value of k is %3D

A:

Q: Determine the absolute maximum and minimum values of f(x) = x²e on x = [-5, 1].

A: Given: fx=x2ex on x∈-5, 1 To find the absolute maximum and absolute minimum of the given function on…

Q: Find the maximum and minimum values of g(x) =1+ x + x2 + x³ + x4 + x on the interval [0, 2].

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Q: If f'(x) = x - 2x-x +2, thenf has a relative minimum at x= -2 O0 0 O0

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Q: Suppose f'(x) =x++x³- 6x². Determine the value of x where f has a relative minimum value. O x=0 O…

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Q: 3. Find the absolute maximum and absolute minimum of f(x) = 2x³ - 6x +1 on [0,3].

A:

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

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Q: If an odd function f(x) has a local maximum value at X=c which of the following must be true?

A:

Q: The function F(x) = 2x^3 + 3x^2 has a relative minimum point at x =

A: We will solve the problem

Q: For the function f(x) = x³ – 27x, its local maximum is which occurs at ( its local minimum is which…

A:

Q: )For the function f(x) = x-48x, its local maximum is which occurs at ( ... its local minimum is…

A: Solve by derivative test

Q: Suppose that f ‘(x) is negative for x 1. Does f have a local minimum or maximum value at x = 1?

A: The answer is 'YES' Let see how it is YES in next step.

Q: (3) Find the absolute maximum and minimum values of f(x) = x³ – 3x – 1 on the interval [0,3).

A:

Q: If f(x) = x3 – 6x² + 9x + 15 then the minimum value of f(x) over the interval [0, 6] is

A:

Q: Suppose that  3 ≤ f ′(x) ≤ 4  for all values of x. What are the minimum and maximum possible values…

A: Given inequality is:  3 ≤ f ′(x) ≤ 4 To find: Minimum and maximum possible values of f(4) − f(1). To…

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: Find the absolute maximum/minimum value for f(x)=x² – 4x+1 on the interval [(-3, 3] 9.

A: Given: fx=x2-4x+1 and x∈-3,3   The Power law: ddxxn=nxn-1

Q: Find the absolute maximum of p(x)=x2 −x+2 over [0,3].

A: We have to find absolute maximum of f(x) in given interval .F(x) is given as:

Q: Suppose that 2 < f '(x) < 3 for all values of x. What are the minimum and maximum possible values of…

A: Use the first inequality and integrate all the values from 2 to 5.

Q: of all real numbers x such that -3 < x < 5. (a) For what values of x does f have a relative maximum?…

A: at x=-3 and x=5 f is relative maximum

Q: Suppose that 2 < f '(x) < 3 for all values of x. What are the minimum and maximum possible values of…

A:

Q: 1) Find the Absolute Maximum and Absolute Minimum for f(x) = x³ 9x² +24x on [0,5]

A: At absolute maximum and minimum of a function y=f(x), its first derivative is zero, i.e. f'(x)=0 (a)…

Q: Suppose f:(x)=x++x³- 6r2. Determine the value of x where f has a relative minimum value. O x=2 O x=0…

A: Function f'(x)=x4+x3-6x2 To find x where f has a relative minimum value

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…

A:

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

A:

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

A:

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: Find the absolute maximum and absolute minimum of the function f(r) = 4x + 3 over 1, 4.

A:

Q: Find the absolute maximum and absolute minimum values of the function f(x) = −x3 + 3x + 7 on the…

A: We find critical points by setting f'(x)=0 x=1 is not in the interval [-2,0]

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: The degree of f(x) is [odd and the leading coefficient is negativev. There are real zeros and…

A: Consider the graph

Q: identify the coordnates of any local maximum or minmum values of the function y=(x+3)2/ e2x

A: y=(x+3)2/ e2x Or, y = (x+3)2e-2x We need to find it's derivative and equate the same to zero.

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: Find the absolute minimum if exists of f(x)=6x^2 −x^3 +8 on the interval 0≤x≤4

A: Use the first and second derivative test and find the absolute minimum of function f(x).

Q: Suppose that f(x, y) = e e-x² - 2y² + x Then the maximum value of f is

A:

Q: what is the absolute maximum/minimum of: f(x)=xln(x/4) on [0.2,4]

A: Given, function is

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

A:

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

A:

Q: Find the absolute minimum value on​ [0,∞​) for f(x) = 2x2 -12x + 6

A: To find the absolute minimum value of the function on the given interval.

Q: What is the local minimum value of the function f(x) = x^3(x + 4)

A: We have the given function as fx=x3x+4 For local maxima/minima, we need to calculate critical point…

Q: If f'(x) = x³ – 2x² – x + 2, then f has a relative minimum at x

A: f'(x)=x3-2x2-x+2, we have to find relative minimum of f.

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.