1 Let f(x) = 1 and g(x) с — 3* Then the domain of f o g is equal to all reals except for two values, a and b with a < b and a = Preview Preview %3D

Q: 8. A function is called even if f(x) = f(-x) and a function is odd if f(x) = f(-x). Suppose that f…

A: To find the following parts,

Q: (a) What are the x-values for which the function appears to be not continuous? O Function g appears…

A: If function g is connected at all points in the given graph , it is continuous for all values of X.…

Q: The function f(x) is continuous on the interval [-1,3]. The table below gives some of its values.…

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Q: The function f(x) on [0, 3 has x2 + 1 absolute maximum is 0.3; absolute minimum is 0 absolute…

A: The given function f(x)=xx2+1 Differentiate the function with respect to x.…

Q: 14. Find constants a, b such that 4 x < 2 f(r) = x - 2 ax? – bx +3 | is differentiable at all values…

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Q: b) Euler's theorem states that f(:) = "lax, X1 +°"/ax,X2 for functions that are homogenous of degree…

A: Homogeneous Function: A function f of two variables x and y is said to be homogeneous of degree n if…

Q: A function f(x) is continuous on the real numbers and has the following features about the point x =…

A: This question is related to Functions, we will solve it using given information.

Q: Let f be the function given by f (x) = sin z cosz on the closed interval [-27, 27]. On which of the…

A: According to question,Given function,fx = sin x cos xx2 -4,Closed Interval : -2π, 2π

Q: 1. Let f(x)= (x– 2)3. Domain fex) i(-o, a) Range fx) : (-0, 0) (a) Determine if there are any…

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Q: 11. Suppose that f(x) is differentiable everywhere and we know that f(-4) : f'(x) > 6 for all x. -2…

A: Part a) To find the least possible value of f(3), By the mean value theorem, Suppose f(x) is…

Q: 3. (a) If f(x) is an even function, pls prove that f'(x) is an odd function. (b)lf f(x) is an odd…

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Q: Find the absolute maximum and absolute minimum of the function f(x)=2x^5/2 /5−2x^3/2 /3−1 over the…

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Q: 1. Let f(x)=x+sinx in the interval [0,2x] a. Determine algebraically all critical values of f(x).…

A: Maxima or minima: f(x) is any function 1) put fx(x)=0, for critical point. 2) Find fxx(x) at…

Q: Let a &gt; 0 be a real number and considerthe family of functions ƒ(x) = sin ax on the interval [0,…

A: Given that family of functions is ƒ(x) = sin ax, on the interval 0,πa and a&gt;0. Answer(a): For…

Q: Suppose that f(x) = 3xV 2x² + 1 (A) Find all critical values of f. If there are no critical v enter…

A: Given  f(x) = 3x2x2+1

Q: 4. Find the absolute maximum and absolute minimum values of f on the given interval and state where…

A: Given function is f(x) x3-3x2-9x +25 To find absolute minimum and asbsolute maximum over the…

Q: 5. If f(x)=3*-9 and g(x)= tanx, then what is the domain of (g+f)(x) on the interval [0,2m]?

A: For the given question, we can write the function (f÷g)(x) as:f(x)g(x)=tanx3x-32Hence, the domain of…

Q: 3 1. Is the function g(x) = if 0 < x < 1, if 1 < x < 4, continuous on [1,4]? on (-0, 0)? 3 – x2

A: As per guideline we have to solve one question

Q: 7. Find the value of the constant k such that the foloowing function is continuous for all values of…

A: Take LHL=RHL

Q: 5. Suppose f is differentiable on all real numbers. Let F(x) = f(e*) and G(x) = e «), Find…

A: we have to find derivative

Q: Let f (x) = ex - e2x. Find all extreme values (if any) of f on the interval [0, 1]. Determine at…

A: Given:  The function fx = ex-e2x. To find:  The maximum and/or minimum value of given function in…

Q: 6. The function f(x) is created by doing a horizontal compression of 3 on g(x). If (7, 3) is a…

A: horizontal compression means horizontal stretch.

Q: 2. A continuous function f is defined on the interval [-2, 2]. The values of f at some of the points…

A: As per our guide line if multiple questions are posted we are supposed to answer only the first one…

Q: 2:46 Find the value of the constants a and b that makes the function continuous. Define x-1 : x

A: Consider the given piecewise function and the condition for the function f(x) to be continuous.

Q: 43) For f(x) a) Give the domain of f b) Evaluate (-2), (0) and /(3) c) Graphf d) Is f continuous on…

A: To determine the nature of the given function

Q: 4) f (x) = fiod the interval Cs) on which %3D graph of f(x) is Concave up (if any)

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Q: 1.βx − 3 if x ≤ 2(b) Suppose that f(x) = βx + 2 if x &gt; 2Find the value of β so that f(x) is…

A: For continuity, left hand limit=right hand limit=f(x)

Q: 00 ak 10. If f(x) = ar(x - 3)* for all real r, then the function F(r) = (-3)*+1 has %3D k=0 k+ 1 k=0…

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Q: all polynomials f(x) of degree at most 4 that satisfy f(2)=0. yes or no?

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Q: Let f(x) = -9+ 8x – a³. (A) Find the critical values of f(x). Critical values: (B) Use interval…

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Q: 8. The function f is defined on the closed interval [0, 1] and satisfies f(0) =f =. =f(1). On the…

A: 8 Given function fx is defined on the closed interval 0,1 and satisfy f0=f12+f1. And fx is…

Q: 1+x2+y2 Determine the set of points at which the function F(x, y) = is continuous. 1-x2-y2

A: In this we have to check Discontinuity of equation.

Q: 1) Determine the value of c such that the function is continuous Vx E R. Show and explain in…

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Q: 5+x Determine the largest interval for which g(x) = is continuous everywhere. %3D x²-2x+1

A: Given: g(x) = 5+xx2-2x+1 To determine: The largest interval for which function is continuous…

Q: 1. Determine whether these statements are always true or sometimes false. (a) The function f(x) |a-3…

A: As per our guidelines, we can answer only one question in a single request. Kindly re-post the other…

Q: 7. For the function f (x) = In(x² + 1) (a) find all intervals where f is increasing, (b) find all…

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Q: 7. Let f(x) = x³ – 6x2 + 5 for x in [-1,3], as in the previous problem. Given that f(x) = 0 when x =…

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Q: 1. Let f(x) = In (x² + 1) %3D Note: 2x and f"(x) = 2(1- x)(1+ x) (x2 + 1)2 f'(x) = %3D x2 + 1 (a)…

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Q: Q 2a. Verify the First Mean-Value Theorem for the function g(x) = x³ +1 on the interval [1, 2]. b.…

A: We’ll answer the 2nd question since we answer only one question at a time. Please submit a new…

Q: f f (x) has a local maximum, but no absolute maximum, in the interval [-5,5], then f (x) cannot be…

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Q: 25. f(x): Determine the value of k so that f(x) is continuous. Show work. 2x² - k x < 2 = 2x² - 5x -…

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Q: 1) determine the value of the constant k so that the function is continuous in x = 2…

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Q: 3. Find constants A and B that make the function continuous and differentiable for all x. Ax x > 1…

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Q: 2. Let f be continuous and differentiable everywhere. Suppose that f(-1) = f(1). Show that there are…

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Q: 3. Let f(x) = 1/r². Then f(-1) = f(1). Explain why it is not possible to use Rolle's Theorem to show…

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Q: Let f(x) be a function that is differentiable for all x. Let g(x) be defined by g(x) = f(x) + f(3 –…

A: (a) g(x) = f(x) + f(3-x) g'(0)=f'(0)-f(3)g(3)=f'(0)-f'(0)g(3)=f(0)-f'(3)  from intermidiate value…

Q: 7. Let f be a function that has first derivative f ((x) = ++2 and second derivative f"(x) =…

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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.