What is the range for the function h(x) = (x 3) + 2? | 0(- 0, 3] 0(- 0, 2] 0(- 00, - 2] | O [2, 00) O [3, 0)

Q: (c) For what values of a and b does the function (ах- 3, x< 4 f(x) = } (-x? + 10x - b, x24 satisfies…

A:

Q: Where is the interval increasing and decreasing. Which interval or union of intervals represents the…

A:

Q: Find the absolute extrema of the function on the closed interval.

A: Given: To Find: Absolute extrema of the function on the closed interval. Concept:

Q: 1. F(X) = 2X3-6X2-18X+2   {-2,4}

A: Given:  F(X) = 2X3-6X2-18X+2   {-2,4}

Q: 48. f(x) = x 6x2 + 5, [-3, 5]

A:

Q: Find the absolute maximum and absolute minimum values of f on the given interval. f(x) = (x2 - 1)3…

A: Here we will find the value of the function at all the critical points and the ends of the interval…

Q: Find all absolute and relative extreme values of the function f(x) = -x° + 2x2 - x - 1, on the…

A: Here we have to find the relative and absolute extreme values

Q: find the extreme values on the interval f (x) = x(10 − x), [−1, 3]

A:

Q: Find intervals where f is increasing/decreasing f(x)=x3+3x2-9x-12

A: Given function

Q: *The interval [a, b] for a function x^3 - 4 x- - ...... 9 = 0 is [2,3] O [0, 2] O [0, 1] O [1, 2] O

A: We need to find the interval for a function f(x)=x3-4x-9=0

Q: For f(x)=3|x| does the Mean Value Theorem apply on the interval [-2, 2] and why?

A:

Q: locate the absolute extrema of the function on the closed interval: f(x)= x^2/ x^2+3, [-1,1]

A:

Q: The Range of f(x) = V1-x is 1. [-1, 0) 2. (-, 1] 3. (-0,0) 4. [0, 0) 1 2

A:

Q: What is range of function f(x) = x-1 which is defined everywhere on its domain? * (-00, 00) – {0}…

A: Topic:- range and Domain of function

Q: Explain why you can not apply the mean value theorem to the function f(x) = x2/3 on the interval…

A:

Q: Find the absolute minimum and absolute maximum values of f on the interval below. f(x) = 2x4 - 4x² +…

A: We need to check value of f(x) on critical points and boundary values to absolute minimum and…

Q: 81. A function y = f(x) is increasing on the interval (0,5). What conclusions can you draw about the…

A: If a function is an increasing function then this means when the value of the variable x increases…

Q: 9. The interval for function (6-x)/4< (3x-4)/2 is

A: Find your answer below

Q: Find the absolute maximum and absolute minimum values of f on the given interval. g(x) = x +-,4]

A: here we need to find absolute maximum and absolute minimum values of given function . the solution…

Q: Find the absolute extrema of the function f(x)= (x+2)4 (x2 -8)2  on the interval [-4,1].

A: Given,f(x)=x+22x2-82 An absolute extremum of a function in a given interval is the point at which a…

Q: nd the absolute maximum and absolute minimum values of f on the given interval. f(x) = 6x3 − 27x2 −…

A: Given function is  fx=6x3−27x2−72x+4 To find the absolute maximum and absolute minimum values of f…

Q: If f(x) is an even function defined on the interval [-5,5], Then find - X+1 the real values of x…

A:

Q: Explain why the Mean Value Theorem does not apply to the function f on the interval [0, 6].

A: Consider the function: fx=1x-3. Mean Value Theorem states that if a function is continuous on a,b…

Q: Find the absolute maximum and absolute minimum values of f on the given interval. f(x) = 2x3 − 3x2…

A:

Q: Part III: Use the graph of f(x) to sketch y = f(x) 5 4 하 2 6 -5 -4 -3 -2 123456 -3 4 -하 -6

A: Given: y=f(x) To draw: y=0.5f(x)

Q: 1. Find the absolute extrema of f (x) = x* - 8x² + 3 on the interval [-1,3].

A: Absolute extrema on a closed interval lies on end points or at f'(x) = 0 So first we have to…

Q: (c) For what values of a and b does the function ах 3, x < 4 f(x) = (-x² + 10x – b, x 2 4 satisfies…

A: Answer:   a = 0 and b = 27

Q: Find the absolute extrema of the function on the closed interval.                         f (x) = 3…

A: Given equation is   f(x) = 3-x The absolute maxima or minima occur either on the critical points or…

Q: The range of f(x)= 3+|x| is O (0,3] O (3,0) • 13, x) O (-x,3) 1Tx,3] (-x,3]

A: Explanation of the answer is as follows

Q: (c) For what values of a and b does the function (ах— 3, x 4 satisfies the conditions of the…

A: Function  To find the values of a and b for which f(x) satisfies the conditions of the Mean-Value…

Q: Find the absolute extrema of the function on the closed interval.

A: We have to find absolute extrema of the function on the given close interval: fx=x3-32x2,    -1, 2…

Q: Find the absolute minimum and absolute maximum values of f on the interval below. f(x) = x4 - 8x2 +…

A: First we find the value of the function at the critical point and then at the corner points Then we…

Q: (c) For what values of a and b does the function ах — 3, x < 4 f(x) = (-x² + 10x – b, x2 4 satisfies…

A:

Q: 3- x, 3. f(x) = [-1,4] 3+x, x > 0 1 4. g(x) [-1, 2] .2 - 4

A:

Q: Given the function of f(x) = -3 – in the interval [-8, –2], find a point x = c between -8 and -2 so…

A:

Q: For what intervals is f(x) = x* – 8z² +3 decreasing? O The graph is decreasing on the interval (0,…

A: givenf(x)=x4-8x2+3f'(x)=4x3-16xf'(x)=4x(x2-4)so critical points will be -2,0 and 2

Q: Find the absolute maximum and absolute minimum values of f on the given interval. f(x) = 2x^3 − 3x^2…

A: Given,           f(x) = 2x3 − 3x2 − 36x + 3  and interval is [-3,4].

Q: Located the absolute extrema of the function on the closed interval. f(x) = x³ -x²,[-1,2] 5. g(x) =…

A: NOTE: Refresh your page if you can't see any equations. . to find the critical point take…

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

A:

Q: Located the absolute extrema of the function on the closed interval. 4. f(x) = x3 -x² ,[-1,2]

A: According to our guidelines we are supposed to answer only one question since you have asked…

Q: Find the local and absolute extreme values of the function on the given interval.    f(x)= square…

A:

Q: Find the interval on whih f(x) =x2-3x+8 increasing or decreasing

A: Given,        fx=x2-3x+8

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

A:

Q: 2. Find the absolute max and min of the function f(x) = x° (x-4)² on the interval -1,5] using the…

A: The given function: f(x)=x45(x-4)2 The interval is [-1,5] To find the absolute maximum and minimum…

Q: Explain why the Mean Value Theorem does not apply to the function f on the interval [0, 6]. f(x) =∣x…

A: Mean Value Theorem: Let f be a function satisfying two condition: 1. f is continuous on a,b. 2. f is…

Q: Find the absolute extrema of the function on the closed interval.                      g(x) = 3√x,…

A: g(x) is continuous on the given interval.  So, the absolute extreme exist and must occur either at a…

Q: Evaluate f''(c) at the point. f(x) = (x2 - 5)(x3- 5), c = 1

A:

Q: Find and classify the extreme values of f(x)= 6x* –4x° over the interval [-2,2].

A: Given,  f(x)=6x4-4x6

Q: Locate the absolute extrema of the function on the closed interval. 4. f(x) = x3 -x2 ,[-1,2]

A:

Q: Explain why the Mean Value Theorem does not apply to the function f on the interval [0, 6]. f(x) =…

A: Given: f(x) = 1/(x − 3) and f in on interval [0,6]

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.