Determine f (x) for the following function. f(x) = Vx + 6+ 3

Q: Find f'(a). f(x) = V1- 6x f'(a) =

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Q: Find the maximum and minimum values of the function f (x) -3x on the interval 1+x2 0<x<6.

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Q: The function f(x) = Vx – 2 + V4 – x is.

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

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Q: 12. For the function f(x) = x² + 10x + 7, x ER, find any global maxima or minima points

A: If y=f(x), then the independent variable x is called the input of the function and the dependent…

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

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Q: The domain of the constant function g (x) = k is ________, and its range is _______ .

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Q: A function f(x) = v1 – x² is

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Q: =V find f(x). 3/ x7 For the function f (x) = ,find f-1 (x).

A: Given function,f(x)=x753 ,we have to find f-1(x)

Q: Let h(x)=f(x)g(x). If f(x)=x2−3x,g(0)=−1, and g′(0)=−4, what is h′(0)?

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Q: snip

A: Make the changes function in the  function (f+g)(x) by adding and subtracting terms such that…

Q: Find the domain of (f • g) where f (x) and g (x) = Vx + 4.

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Q: Find the domain of the function. 29) f (x) = v25 – x2 30) f (x) = 3x + 4 31) h(x) 32) h(t) = |t + 1|…

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Q: Find f"(x) for the functions x² +5x f(x) = ex b. f(x) = (x² – 1)e* a.

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Q: What is the change of y with respect to x of the function s(x) = (3x¹ + 9x³)(x² - 6x +9) ? -9x²…

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

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Q: 2 2 V1-x 1-х

A: ∫un du = un+1n+1+C ∫cos(au) du =1asin(au)+C

Q: Find the absolute maximum and minimum of the function f (x) = x³ - x+2 on the interval [0, 3] %D

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Q: Find a function f(2) such that f (x) = e + 7x and f(0) = - 1 f(x) =

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Q: Find the domain of the function f(t) = V1- 21 – 3Vī+ 6.

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Q: Find f'(a). f(x) = V3 - 2x f'(a) =

A: The given function is fx=3-2x Use the chain rule of differentiation f'x=d3-2xd3-2x×d3-2xdx…

Q: For the function f(x) = 3* find f(x-2) Compute *t1®if f(x) = ax +b h

A: 1. The given function f(x)=3x2. f(x)=ax+b

Q: Consider the function y = (x) where f(x) = x³ +2x2 - 4x and g(x) = x2 + 2. Determine a) the domain…

A: The domain of definition of a function is a set of those values for which we can define a function.…

Q: 2. For f (x) 1, g (x) = 1 + Vx, find the domain and range of f / g, and g/f

A: Given: fx=1, gx=1+x

Q: 2 For the function f(x) = -x', find f'"(x), f'"(0), f'"(1), and f"(- 1).

A: To find the double derivative for the given function.

Q: Find a function f(x) such that f'(x) = 4e" – 3x and f(0) = 4 f(x) =

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Q: 1. Determine f'(x) for the following functions: f(x) = (x2 – 3x)5 b. f(x) = V1-x²

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Q: For function f (x, y) = y2 x2 +1

A: Please refer the attached image for complete solution.

Q: Express the given function h(x) =1/(2x - 3) as a composition of two functions f and g so that h(x) =…

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Q: Let f(x)=2-3x. Find f(t). f(t) = ]

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Q: Let h(x)=f(x)+g(x). If f(x)=6x and g(x)=3x^2, what is h′(−1)?

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

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Q: F(x)=Vxg(x)+3x, with g(1)= 1 and g'(1) 4, then F (1) is

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Q: F(x) =/4 – Vx

A: Given data is : fx=4-x     To find domain and range of function fx

Q: Find the local extrema of the function f(x)=x3−12x.

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Q: For function f (x, y) = x2+1

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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: What is the value for k if f(x) =x² + kr + 13 is an even function?

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Q: Let h(x)=f(x)g(x). If f(x)=−3x2+2x−3 and g(x)=−3x2+4x+3, what is h′(1)?

A: Given:h(x)-f(x)g(x)f(x)=-3x2+2x-3g(x)=-3x2+4x+3

Q: Find a value of x such that f '(x) = 0.  with the function f(x)=x squareroot x+1

A: Given function is fx=xx+1  To find value of x such that f'x=0. Solution: Differentiating the given…

Q: Find f'(a). f(x) = V2 - 6x f(a) =

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Q: (1) For the function f(x)=x+1/x2+3,evaluate and simplify the following: (d) f (ab−1)

A: The given function is  f(x) = (x +1) /(x2 +3)

Q: The function h is defined by h(x) = x^2 +2. find h(5z)

A: Given h(x)=x2+2

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

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Q: For the function f(x) = (E)', find f-'(x). 8 Of (x) = (8/") || 4 Of (x) = (V8x)* f1 (x) = V (8æ)“…

A: Solution: The objective is to find the inverse of the given function

Q: Find the x-values of the stationary points of the function  f(x) = x^4 + 4x^3 - 4x^2 - 24x

A: Given: f(x)=x4+4x3−4x2−24x

Q: What is the domain of the function f(x) = %3D 5" Vn n-1

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Q: f(x) = v x² + 5x - X

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Q: Find f'(x) for f(x) = 2x°e*. f'(x) =

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Q: The domain of the following function is f(x, y) = 1 – /2y – -

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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.