3 - The real value of a function f(x) which corresponds to the value of xo is 5. The result which is obtained by the polynomial approximation is 5.05. What is the percentage relative error of this approximation

Q: Compute and completely simplify the difference quotient for  f(x) = √x+6   f(x + h) − f(x) h =

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Q: Simplify the difference quotient g(x)=f(x+h)-f(x)/h when f(x)=1/x. What happens to g(x) as h -> 0?

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Q: Differentiate the function f(x) +5r DO NOT simplify or factor %3D (7-z)31 quotient 012 Your answer…

A: We have to find derivative

Q: For the function f(x)=x to the power of 2+1 when x=2 the f(×)

A: Given,             For the function fx=x to the power of 2+1.To find : The value of fx when x=2.

Q: find the inflection points of f(x) = (x-2)4/3

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Q: What is the range of the rational function f(x) = 1/x?

A: Given rational function is ,                           f(x) = 1/x  Range : Range of a function is…

Q: Evaluate f(x) ƒ(1) = f(x + 7) = f(x) + f(7) f(x + h) = = = x + 2 at the indicated values.

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Q: f(X) = 2/X       g(X) = X+1/9     (What is the domain?)

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Q: Explain why both f (x) = x/ (1- x4) and g(x) = p are algebraic g(x) = -x / √(1-x4) functions.

A: f(x)=x1-x4 and g(x)=-x1-x4

Q: By carefully showing all your steps, differentiate the function f(x) = (tan−¹(x + √√x)) 4

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Q: f(x)=(1.55)^x+9 for x=8.43 Evaluate the following function for the given value of x.

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Q: Evaluate f(x+h)-f(x) h , given f (x) = 5 x+2 Use a / to represent a fraction line. Do not include…

A: The function is given byTo determine: The expression of .

Q: Explain how f (x) = (x − 1)2 + 3 is obtained from f (x) = x2.

A: Given f(x)=x^2, to obtain f(x)=(x-1)^2 from f(x)=x^2 we have to shift the graph to 1 unit right.

Q: Compute the difference quotient (a) f(x) = -3+7x (b) f(x) = 5x²5x+2 Submit Question f(x + h) − 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.