1. Find the open intervals where the function is increasing and the intervals where the function is decreasing. Determine the relative extrema of the function. f (x) = x3 – 5x² + 8x

Q: Find the critical points of the function f(x)=x4−5x4+5x3−1.

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Q: Find the absolute maximum and minimum of f (x)=x* – 2x -x - 4x +3 on the closed interval [0, 4]. а.…

A: fx=x4-2x3-x2-4x+3 Differentiating wrt x, we get  f'x=4x3-6x2-2x-4 Putting f'x=0, we get…

Q: 4. Find the values of x for which the line tangent to the graph of f(x) = 3x2 – 4x + 8 has a tangent…

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Q: Given the piecewise function: 4x + 12 { x<-2 - 1<x f(x) = -2x + 6 18. What is the interval of the…

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Q: find the critical points for the function f(x)= 2x³ – 3x² – 72x-11

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Q: 3. Find the absolute maximum and absolute minimum values of f(x) = 2x´ - 4ln(x) on the | interval […

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Q: 4. Find the values of x for which the line tangent to the graph of f(x) = 4x2 – 8x + 4 has a tangent…

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Q: Find the absolute maximum and absolute minimum values of the function: f(x)=5x^7−7x^5−7 on the…

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

Q: Determine critical points of the function f(x)=∣∣x2−4x+3∣∣.

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Q: Find the critical points of the function f(K)-7x2-14x.

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Q: 6. Determine the absolute maximum values of the function f(x) = x³ – 6x –1 where xe [-2,3]

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Q: 22. Find the maximum or the minimum value of f(x)=-2x² –10x+5. SLO 11

A: To find the maximum and minimum values of the function

Q: Find the maximum and minimum values of the function f(x) = x² – 6.x +7 on the interval [0, 5].

A: It is given that, f(x)=x2-6x+7   , on the interval 0,5We have to find the maximum and minimum values…

Q: Find the absolute maximum and minimum values of the function over the indicated interval. f(x) = 4x²…

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Q: 14. Find the minimum value of the function f(r) = x + 4x + 5. -2 5 1.

A: Given function: fx=x2+4x+5 To determine: Minimum value of the function.

Q: Find the absolute maximum and absolute minimum values, if any, of f (x) = x³ + 3x² + 1 on the…

A: Absolute maximum point is a point where the function obtains its greatest possible value. Absolute…

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

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Q: 5. Find all relative maxima of the given function. y =x* -8x' +16x² +3

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Q: For what value of x does the function f(x) 4x attain the absolute minimum = in the interval [-3,5]?…

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Q: Find, if any exist, the critical values of the function f(x) = x* – 8x³

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Q: Find the absolute maximum and absolute minimum of the function f(x) r2-6x + 5 over (1, 6].

A: Given function: fx=x2-6x+5 To find: Absolute maxima and absolute minima over 1,6.

Q: 4. f(x)= 3x5 + 5x³

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Q: 3. Find the stationary points (local maximum and local minimum) of the function f(x) = -3x3 + 3x² +…

A: Solution:Given  f(x)=-3x3+3x2+3x+6To find Stationary points of the given function:Formula:dfdx=0…

Q: Determine all critical points for the function. f(x) = x 3 - 12x -2

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Q: Find the absolute maximum and minimum values at the indicated interval f(x)=x^2-6x-3 ;[1,6]

A: Given function is: First find the critical points of the function by putting:

Q: Find the absolute maximum and absolute minimum values of f on the given interval. f(x) = x3 − 6x2 +…

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Q: Find the absolute maximum and absolute minimum values of f on the given interval. f(x) = 6x3 − 9x2…

A: Given that f(x) = 6x3 − 9x2 − 36x + 8,     [−2, 3] To Find the absolute maximum and absolute minimum…

Q: The interval in which the given function is decreasing is at y = x3 – x2 – 5x – 4

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Q: If f (x) - 2x - kex has a relative maximum at x = -2, then the value of his

A: Given  f(x)=2x-k.exNote: As there is no h in the equation it is assumed that we need to find…

Q: Determine the absolute extreme values (maximum and minimum) of the function f(x)=Vx² -4x+13, for…

A: Topic:- application of derivatives

Q: 3. Find the absolute maximum value of the function f(x)=- 1+x2

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Q: For what value of x does the function f(x) = -x3 – 4x attain the absolute minimum in the…

A: The value of function which is least in entire range of function is called minimum value of…

Q: Find the distance between the local maximum and the local minimum values of the function f(x) =x -…

A: n order to find maxima and minima of a function , we have to follow the two stepsStep 1:  Find the…

Q: 1. Find the maximum and minimum limits of the function: f(x) = 5x3 + 2x2 – 3x %3D

A: We have to find the maximum and minimum limit of the given function.

Q: find the absolute maximum and the absolute minimum valves of the function, if they exist, on the…

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Q: Find the absolute maximum and absolute minimum values of f on the given interval. f(x) = 6x3 − 18x2…

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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: find the absolute maximum and minimum values of the function f(x)= x^4-2x^2+1 on the interval [0,3]

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

Q: Find the maximum value of the function (x1 + 4.x2)² f(#1, x2) = by expressing f (x1, x2) as the…

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Q: find the exact location of all the relative and absolute extrema of the given function: g(x)= 2x^3…

A: find the exact location of all the relative and absolute extrema of the given function: g(x)= 2x^3…

Q: Suppose f'(x) =x++x³– 6x². Determine the value of x where f has a relative maximum value. (A x= -3 B…

A: The solution are next step

Q: Find the absolute extrema of the function on the closed interval.                       g(x) = ∣x +…

A: Consider the given function, gx=x+4 over the interval -7, 1 differentiating the above function we…

Q: Find the global extrema of the function f(x)=3x4−6x2+2 on the interval [−2,2]

A: Global extrema of a function exists at critical points or at the end points of the interval.…

Q: Find the absolute maximum and absolute minimum values of the function, if they exist, on the…

A: Check Maxima and minima by first and second derivative.

Q: 3. Given the function g(x) = x - 2x2 + x, find the interval(s) when g is concave up and decreasing…

A: We have given a function g(x).  We have to find the interval where g is concave up and decreasing at…

Q: 8. Given the function f(x) = -x³ + x² a) Determine the intervals in which the function is increasing…

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Q: B4: a) Find and classify all critical points of the function f(x) = x³ + 3x² – 12x + 5

A: In the question we have to find critical points.

Q: Consider the function f(x) = 0s xs 2. 9x2 +1' This function has an absolute minimum value equal to:…

A: To find absolute maxima and minima on the interval [0,2] for the function: f(x)=-x9x2+1