Consider the image attached of the graph of a function y = g(x) on the domain -8 <= x <= 8, which consists of line segments and semicircles of radius 3 connecting the points (−8, 0), (−6, 6), (0, 6), (6, 6), (8, 0). What is the multipart formula for y = g(x) when -6 <= x <= 0 and when 0 <= x <= 6?

Q: h(x)=x^2-3x+5, find x and y intercepts

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Q: Write the length L of the rectangle as a function of y.

A: The length of the rectangle can be determined by using the fact that one end is always on y axis and…

Q: Evaluate Function  g(3,4) when g(x,y)=x-6y/x^2+y^2 a. -25/21 b. -5/21 c. -21/25 d. -21/5

A: For this problem, we have to substitute the values of x and y in given function g(x,y).

Q: Differentiate the following function. y=x(x5 + 5) 3 Choose the correct setup below to differentiate…

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Q: Let f (x) = x / x - 1 and graph the function f (f (x)) in the window [ -15, 15] by [ -10, 10]. Trace…

A: Consider the provided function, fx=xx-1 Find the formula of ffx. We can write as, ffx=f∘fx. So,…

Q: The function f(x)= x^2 - 6x+4 on which interval will f(x) have a root?

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Q: f(x)= 3(x+5)^2-1; (-4,2)  what's the axis of symmetry

A: Solution: For a quadratic function in a standard form ax2+bx+c The axis of symmetry is a vertical…

Q: If f(x)=x^2 and g(x) is the graph of f(x) shifted to the right 3 units, stretched vertically by a…

A: When f(x) shifts 3 units right then it becomes f(x-3)

Q: Sketch the graph of:

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Q: Consider the function F(x)= (x+2)^2 for the domain [-2, ∞)

A: Given           Function is :                            F(x)=(x+2)2 for the domain [-2, ∞)   To…

Q: The graph of y = f(x) is transformed by a horizontal expansion by a factor of 4 and a vertical…

A: Use transformation of functions

Q: The graph of y = 3(x - 2)3 + 2 always increases except at 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.