Use the following function rule to find f(0). f(x) 10(4)* + 2 %3D f(0)

Q: Find the value k that makes the function continuous. (ka?, x > -2 f (x) kx + 18, x < -2

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Q: Find the value of the constant k that makes the function continuous.

A: A function is relation between set of inputs and output. The piece-wise function is a function which…

Q: Given the function f(x) = Vx5 – 3Vx2, find the interval(s) of increase.

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Q: Find f'(x) for f(x) = e5a+2x

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Q: (a): Find the critical points of the function f(x) = 6x? – 12x. -

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Q: Find all antiderivatives of function:  f (x) = 9x8

A: Anti-derivative of a function is given by the integration of the function.given function f(x)  -f(x)…

Q: (f) What is the first-order condition implied by unconstrained maximization of I1 X 1333 X, where x…

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Q: Find Fxxygy for the function Fory)-J*J€nx-x]

A: We havr to find the derivative.

Q: If f(x) = | V17+t³dt, then what is f(-1)?

A: Leibnitz Rule: Let f(x) be a differentiable function on closed interval a,b such that a,bare the…

Q: Find f'(0) for f(x) x = 0. 0,

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Q: Describe how you could use the graph of f(x) = 2" to obtain a decimal approximation for V2.

A: y=2x

Q: Find the linearisation of f(x) = 4√x at a = 16. Use this to estimate 4√ 15

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Q: For f(x) = 2x² + 5x+", find. 10 S(a +h)- f(a) if h +0. h

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Q: The antiderivative of the function f(x) .2+9x is. 8.

A: We use basic integration method to solve this Question

Q: 2. What is the domain of the function f(x) Vx + 4

A: we have to find the domain of the function. f(x)=x-2x+4

Q: Find the graph of the function f(x) = [x] + [x/2] from R to R.

A: Given function is fx=x+x2. Definition: Floor function is the greatest integer that is less than or…

Q: What is the domain of f (x) = ln(x – 3) + 4?

A: Domain where fx is well defined.

Q: Find the points of inflection of the function f(x)=e−x2.

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Q: Given the piecewise function defined below, determine the value of f (x)dx in simplest form. -6x² +…

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Q: Why is f'(x) approximated well by the difference quotient when Ax is very small?

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Q: Q2:Find the relative extrema of f (x) = 3x³ – 5æ³ Suhmit

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Find f '(x) given that f(x) = 2+5x 3x3+4 %3D Show your work

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Q: Find the value of a so that f(x)= x2 + a has a range of [-2, ∞).

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Q: If f(x) = x° and g(x) = 0.5f(x), what is the value of g(x) at x = 2? %3D

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Q: Find the values of x for which the function f (x) = x −7/x^2 + 3x −70 is continuous.

A: Topic:- function

Q: Find the net change in f(x) on – 4.5 < x < 4.5 where: f'(x) = V81 – x2

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Q: (a) f(x) = 2r3(3 – 4x)

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Q: Find f'(a) for -7 f(x) = V11 – 9a f'(a) = %3D

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Q: Consider the function f(x) = z + 6

A: Givenf(x)=1x+6

Q: Find the relative extrema for f(x) = x* + 32a²

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Q: f (x) = 3.x5 5x3.

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Q: does y=e9-x2-2 exist? whaet is the domain and range of the function if exists

A: Consider  y=e9−x2−2

Q: Find the value for k so that the function will be continuous at x = 2. 4x + 16 if x 2

A: The function fx is continuous at x=a, if limx→a-fx=limx→a+fx It is given that fx=4x+16if…

Q: Let h(x)=f(x)+g(x). If f(x)=6x and g(x)=3x2, what is h′(−1)?

A: Add the given two functions and differentiate with respect to x

Q: If x is large, which function grows faster, f(x) = 2x or g(x) = x2 ?

A: Given,            fx=2x or gx=x2To find : if x is large, then which function grows faster.

Q: Comput: f dx 2+x

A: I am attaching image so that you understand each and every step.

Q: The interval in which the function is decreasing is at x2 бх + 1 2 x3 y = 3

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Q: Find f '(a) for f(x) = 3 − 2x + 4x2

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Q: Find the lineearization L(x) of the function f(x) = x^3/4 at x = 16.

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Q: Let f : Z4 → N be the floor function f(x) = [(x – 1)/2].

A: Given f:ℤ+→ℕ be the floor function defined by  fx=x-12 For x=1,  fx=02=0&lt;1 For x=2 fx=12=0&lt;2

Q: 7. Find f'(x) for the function f (x) = V-3x4 – 2

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Q: What is f'(x) of the function f(x) = 4xy^3 if you consider y as a constant?

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Q: The antiderivative of the function f(x) = .8 + 10x3 is. %3D

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Q: Find the most general antiderivative of the function f(x) = 72° – 6x³ + 3x?.

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Q: #2: Differentiate the following functions. y= 3V3x

A: Derivatives can be defined as rate of change of function with respect to an independent variable. It…

Q: 5. For f (x) 3x 5 and g (x) 6 4x, find (fog) (x)

A: As per guideline we have to solve the problem

Q: The derivative of the function f(x) = 18 is 1 5x 18 5x + 18 18 5x4 + (x) 18 5x4 (교2) 18 5x4 + (23)

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Q: Find the point of diminishing returns (x,y) for the function R(x), where R(x) represents revenue (in…

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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.