Given the function f(x) = –2x4 + 16x³ which f is both decreasing and concave up. - 36x2, determine all intervals on - –

Q: Given f(x) = x4 − 2x2 . Find the intervals of increase or decrease.

A: We find the critical points first  to find critical points we need f'(x) Then set f'(x)=0 and solve…

Q: determine the intervals where H(x) = ( x+2)(x-4)3>0

A: Set H(x)=0 and find x.

Q: Find the absolute extreme values of the function on the interval. F(x) = Vx, -27sxs8

A: We will first differentiate the function to find the critical points.

Q: given the function f(x) = 6 + x + x^3 from [0,2], find the lower sum using four rectangles

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Q: Find the open intervals on which the function is increasing or decreasing.     g(x) = x2 − 2x − 8

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Q: Find the intervals on which f (x) = x2 − 2x − 3 is monotonic.

A: we have to find the interval on which f(x) = x2 − 2x − 3 is monotonic.

Q: Graph the function f(x) = 4x + 2 and determine the interval(s) for which f(x) ≥ 0.

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Q: Find the range and domain of the function, f(x,y) = sqaure root of (36-x2-y2)

A: Given function is f(x,y)=36-x2-y2We have to find the domain and range of…

Q: Find a and b so that the function 1 5x3 — 6х? + 3, х -2 f(x) = ах + b, is both continuous and…

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Q: Consider the function f (x) = x³ – 3x² – 9x + 4 At what interval is the function increasing?

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Q: What is the greatest value of f(x) = 2x3 - 9x2 + 12x   in the interval 0 ≤ ? ≤ 3

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Q: f"(x) = x* + 2x3 – 15x², then on which of the following intervals is f

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Q: Given the function f(x) = x – 15x², find all x-values where f has an inflection point.

A: The given function is fx=16x4-15x2.

Q: Given the function f(x) = x³ – 3x² – 10, determine the absolute maximum value of ƒ on the closed…

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Q: Find the intervals on which f(x) =x2-3x+8 is increasing or decreasing

A: Applying the property of increasing and decreasing

Q: Find the absolute max. and mini. Values by Closed interval method F(x)= -1/x2  0.5≤ ? ≤2

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Q: Given the function f(x) = x³ – 3x² + 3x – 10, determine the absolute maximum value of f on the…

A: We have to find absolute value

Q: Find the open intervals where f is increasing or decreasing.ƒ(x) = x4 + 4x + 1

A: Given: f(x)=x4+4x+1

Q: Given that f (x) = 2x4 – 3x² + 3x + 5, identify the intervals where the function is: (a) Increasing…

A: The answer is given below:

Q: Find the open intervals on which the function is increasing or decreasing.

A: A function f(x) is:  (i) increasing on an interval (a, b) if f'(x)>0 for all elements of a, b.…

Q: Graph the function f(x) = 9 − x2 and determine the interval(s) for which f(x) ≥ 0.

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Q: The function f(r) = x - 18x2 is increasing on the intervals

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Q: Find the intervals on which the function is increasing or decreasing where f'(x) = 4x³ – 4x.

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Q: Find the absolute extrema of the function f(x) = x* - 72x + 1296 on the interval [-7,7].

A: To find: The absolute extremum of the given function

Q: Find the intervals where g(x)= -2(4x+1)10 is increasing and where it is decreasing

A: Find first derivative using exponent rule and chain rule.

Q: Find the open intervals where ƒ is increasing or decreasing. ƒ(x) = x2 + 9x + 8

A: f(x)=x2+9x+8

Q: Find the points of inflection and the intervals on which f (x) = 3x5 − 5x4 + 1 is concave up and…

A: Consider the provided function, fx=3x5-5x4+1 Find the points of inflection and the intervals. For…

Q: Find the intervals on which f(x)=2x/x^2+9 decreases

A: We have to find interval where f(x) is decreasing .f(x) is given by

Q: Find the open intervals where f is increasing or decreasing.ƒ(x) = x2 + 9x + 8

A: Function calculator: f(x)=x2+9x+8 To get maxima and minima we get f'(x)=0

Q: Find the intervals on which the function f(x)=x3+1x3 is strictly decreasing.

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Q: State positive and negative intervals for f(x)=¯ -2x-5 3x+18

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Q: Find the intervals on which ƒ is increasing and the interval on which it is decreasing.

A: Given function is fx=2x5-15x44+5x33. Differentiating the given function with respect to x, we get…

Q: For f(x) = 4x3+ x4/3. determine the intervals where the function is %3D increasing

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Q: Find the intervals on which the function f(x) = x² – 6x + 10 is increasing and decreasing.

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Q: (-2x² – 5x + 14,x 3 x= 3 continuous at x = 3. Justify the conclusion.

A: For given function f(x) ; -2x2 -  5x  + 14  , x < 3   .... (i) 19  , x = 3         ..... (ii)…

Q: Find the intervals on which f is increasing and decreasing. fox) = 3x* - x² + 9

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Q: Find the intervals where f(x) = x* + 2x3 – 3x2 – 4x + 4 increases

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Q: Determine the intervals where y = x3 + 3x2 - 9x is increasing and decreasing

A: Given: y=fx=x3+3x2-9x we know that any given functionfx is increasing if f'x is greater than zero…

Q: Given the function f(x) = x³ + 3x² + 3 - 4, determine the absolute maximum value of f on the closed…

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Q: 3. Given f (x) = 5x² and g(x) = Vx – 3 , what is the domain of (f • g)(x)? Write your answer in…

A: f(x)=5x2, g(x)=x-3

Q: For the function f(x) = 2x6 – 3x4, find the intervals on which it is concave down.

A: Given, f(x)=2x6-3x4

Q: What is the upper and lower limit for the function : f(x) = −12x2 − 37x − 21

A: The function f(x) is a rule that associates or fixes a number to the particular point x. If y=f(x),…

Q: Determine intervals where f is concave up and concave down. f(x) = x3 - 15x² + 8x + 2

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Q: Find the value of the constant ( a, b, or c) that makes the function continuous.

A: Given, f(x)=2x+9x-1x≤3-4x+cx>3

Q: Given f(x) = x4 − 2x2 . Find the intervals of concavity

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

Q: Find the intervals of concavity and the inflection points of f. f (x) = x³ – 3x² – 9x + 2 -

A: Given, f(x)=x3-3x2-9x+2

Q: 4- For f(x) = 4x/3 + x4/3 , determine the intervals where the function is increasing.

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Q: Given the function f (x) = 10 + 5x³ – 3x³, identify the interval(s) where the function is concave…

A: Given:      f(x) = 10 + 5x3 - 3x5

Q: Find the intervals in which f (x) = 2x3 + x2 - 20 x is increasing or decreasing.

A: Follow the procedure given below.

Q: Find the absolute extrema of f(x) = 2x³ – 21x² + 72x on the closed interval [0, 5].

A:

Minimization

In mathematics, traditional optimization problems are typically expressed in terms of minimization. When we talk about minimizing or maximizing a function, we refer to the maximum and minimum possible values of that function. This can be expressed in terms of global or local range. The definition of minimization in the thesaurus is the process of reducing something to a small amount, value, or position. Minimization (noun) is an instance of belittling or disparagement.

Maxima and Minima

The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.

Derivatives

A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which one would be easier? Walking on the road would be much easier than climbing a mountain.  

Concavity

In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the first derivative test and second derivative test to understand the concave behavior of the function.