:)A function g is defined as follows: x, x<-2 g(x)={ px+q, -22 Determine the values of constants P and 4 such that g is continuous on the interval (-*, 00). 1

Q: Verify that the three conditions of the hypothesis of Rolle's Theorem hold for the function f (x) =…

A: 1. f(x) is continuous on the closed interval [a,b] 2. f(x) is differentiable on the open interval…

Q: (3, -13. -mplete the following statements. x) > 0 on the interval(s) x) 0 on the interval(s)

A: Solution of the problem as follows

Q: If f (x) = x² - x and g(x)=√x-2, what is (fog)(x) ? Simplify your answer. x²-x-2 /x² - 2 2-x-2 O…

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Q: b) The difference of two real-valued functions f and is defined by f – g := f + const_1 · g. That…

A: b) We want to express the given definition of the function in terms of two indicator functions. Let…

Q: Which of the following are generally NOT true, for any given function f:X-->Y and subsets A and B of…

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Q: For the function given below, which statements concerning Rolle's theorem are true? Select all that…

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Q: Determine the intervals on which the function f(x) = x (x2 - 175) is increasing or decreasing. 1/3…

A: Given function, fx=x13x2-175 Function f(x) increases where f'(x)&gt;0 Function f(x) decreases where…

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.