Sketch the graph of a function f that is defined over all real numbers and that is decreasing on the interval [-2,3], concave down on the interval (-2, 2), and concave up on the interval (2, 3).

Q: g(x, y) = In(2-x) 1-x2-y²

A: To find the domain of the function, g(x,y)=ln(2-x)1-x2-y2

Q: Sketch a graph of a single function that has all of the following propertie a) Continuous and…

A: Graph

Q: Consider the function f(x) = 2x3 - 6x2 - 18x + 9 on the interval [-2,4]. What is the absolute…

A: Given function - f(x) = 2x3-6x2-18x+9Differentiating f(x) with respect to x - f'(x) =…

Q: f(t) = 3 – 9 ? -6, [-3, 3]

A: To find: The continuity of the function f(t)=3-9-t2 on the interval [-3, 3]

Q: Suppose f is a function defined and continuous on the open interval (a, b). Suppose g is a function…

A: Given that: f is a function defined and continuous on the open interval (a, b).g is a function…

Q: Determine the intervals on which the function is increasing and the intervals on which the function…

A: According to question given thatf(x)=1-x2x

Q: Discuss the continuity of the function on the closed interval.                              g(x) =…

A: We can not have a negative value under the square root.  So,

Q: Determine the open intervals on which the function is increasing and on which the function is…

A: Given function f(x)=x-1x2 ⇒f(x)=xx2-1x2⇒f(x)=1x-1x2

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

A:

Q: Sketch the graph of a function f such that f (x) ≥ 0 on [0, 1] and f (x) ≤ 0 on [1, 2], whose…

A: Consider the function Then and The graph of the function is shown below,

Q: Prove the Theorem: A real valued function on a closed, bounded interval is continuous iff its graph…

A: If we assume that f(x) is unbounded at c , then bisecting the interval [a,b] would give us two…

Q: Sketch the graph of f(x) if ...f'(x)>0 on (2,4) and f'(x)<0 on (−∞, 2) ∪ (4, ∞),f''(x)>0 on…

A: Here we suppose that the given function is continuous on the given intervals and differentiable on…

Q: Let f (x) = x³ – a* with domain (-∞, ∞0). Find the intervals where f is increasing and where f is…

A: Given,           fx=x3-14x4 with domain -∞,∞.

Q: Sketch a graph of a function ƒ, where ƒ(x) < 0 and ƒ′(x) > 0for all x in (0, 1)

A: Given that, ƒ(x) < 0 and ƒ′(x) > 0 for all x in (0, 1). The f '(x) >0 on (0, 1) implies…

Q: find the interverse of the function on the given domain. (Enter the domain using interval notation.)…

A: For (a),

Q: A true statement for the function f(x)=2x²-3x²+10 is.. f decreasing on the intervals (-,0) and (1,-)…

A: f(x)=2x3-3x2+10

Q: What is the function f on (a, b) if for all x1, X2 in (a, b) when x, f(x2). is it decreasing or…

A: for all x1 , x2 in a,b when x1<x2 then fx1>fx2 claim- is it decreasing or increasing

Q: Let g be a function with domain the rational numbers, defined byg(x) = 2/x - √,2for rational x. Is g…

A:

Q: Compute f(-4) for the function f defined below. x <0 f(x) = 1x2 - 9, x20 %3D

A: Given Function : f(x)=6xx&lt;0x2-9x≥0

Q: Apply the Mean Value Theorem for the function f(x) = 5x* – 3x – 2 over the interval [-1,2]. Show…

A:

Q: Consider the function f(x)=4-5x2 on the interval [-1,8]

A:

Q: Assume that for a function f(x), f'(x) « O on the interval (-0, -5) and f'(x) » O on the interval…

A: From the given definition:  f ' (x) &lt; 0 when x &lt; -5 so graph must be decreasing in this…

Q: A box with an open top is to be constructed from a rectangular piece of cardboard with dimensions 36…

A: Given that:   (1)                                                (2)

Q: An even function is symmetric with respect to the________

A: An even function is symmetric with respect to the________

Q: Select the graph of a function f that satisfies f' 0 on (-0, -1)U(-1, 0).

A: means f is decreasing for x&gt; - 1   means f(x) is concave up on both sides of x=-1

Q: Oz(-@) and Ør(@) are conjugate functions. That is, Px(-@) =Øx°(@) %3D and Oz"(-@) = , (@)

A:

Q: Sketch a graph of a function ƒ, where ƒ(x) &gt; 0 and ƒ′(x) &lt; 0for all x in (0, 2).

A: Concept:   The calculus helps in understanding the changes between values that are related by a…

Q: Sketch the midline and the graph of the function f(x) = 2 - 3 sin %3D 8- 7- 5- 4- 3 -5 -4 -3 -2 -1 4…

A:

Q: Consider the graph of a function f on the interval [0, 4).

A: We have to conclude about local extreme value of f from the graph.

Q: Let f be a 1-1 function be defined by f={(-2,-1), (0,2), (2,5), (5,-3)}. What is f^-1 (5) ?

A:

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

A:

Q: A piecewise function f is defind by [1-x, x1.

A:

Q: If f(x)<0 for all real numbers x, then f is decreasing on(-♾,♾) True or false

A:

Q: Prove that all functions can be written as a sum of an even function and an odd function

A: Show that: w(x)=u(x)+v(x) and also show that: u(x) is even and v(x) is odd,

Q: Discuss the continuity of the function g(x) = 1/(x^2-4) on the interval (0, 2] and [−1, 3].

A:

Q: A box with an open top is to be constructed from a rectangular piece of cardboard with dimensions 11…

A:

Q: Consider the following function and closed interval. f(x) = x3 - 4x2 – 16x + 5, [-4, 4] Is f…

A:

Q: Verify Mean Value Theorem for the function f (x) = -6x+x3 over the interval [1,3].

A: f(x)=-6x+x3

Q: Find a function for which f'(x) exists for all real numbers but f"(x) doesn't exist for all real…

A:

Q: Find the first 3 Iterates of the function f(x) = - 2x + 3 when x 3 =0 . 3, - 3, 9 - 2, 0, 2 2 z, -…

A:

Q: Sketch a graph of the function f that is continuous on (- 00,00) and has the following properties.…

A: Given, Graph of the function f(x) is continuous on-∞,∞ y=f(x) and has the following…

Q: estimate the type of the function at the interval {(1,2), (2,5), (3,5), (4,7)} is it: 1-1 or onto..?

A:

Q: 9 Determine the domain of the function f(x) 5 - Domain (in interval notation):

A: Solve for the domain

Q: From the graph of f, indicate the intervals on which f is continuous. 6+ 2+ -6 -2 -2+ 4+ O (-00, 2]…

A: Your second option is correct ...at x=2 graph is discontinuous so in the interval x=2 is…

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

A:

Q: why the function is continuous at every number in its domain. State the domain.

A:

Q: Sketch the graph of the function with the given conditions: f has domain [-1,1), f(-1) =-1, f(-})…

A:

Q: Determine the continuity of the function at the given points. forx =-1 %3D f(x = - 2, for x -1 at x…

A: If function f is continuous at x=a then limx→af(x)= f(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.