Find the maximum area of a rectangle inscribed under f(x)=16-x2 and the x axis

Q: Find all zeros of H(x)=5(x-2)^2(x^2-4x-3). Show work and simplify.

A:

Q: Let f(x) = 5x^3 + x + 1. If f(2) = 43, then (x − 2) is a factor of f(x).

A: f(x) =5x3+x+1

Q: A quadratic function is defined by f(x) =x^2+(k+2)x-12 where k is a constant. It is given that the…

A:

Q: Find all zeros for... F(x)=2x^3+3x^2-20x

A: Here is the solution

Q: Differentiate f(x) = (8x³ + 4x )(2x² +5) using product rule.

A:

Q: find the local maximum value of the function xy-x^2-y^2-2x-2y+4

A: The given function

Q: A ball is thrown upward and outward from a height of 7 feet. The height of the​ ball, f(x), in​…

A:

Q: Calculate the relative minimum and maximum of the following equation f(x) = 8x^3 - 13x^2 - 6x -8 and…

A: Step 1: Step 2: Step 3: Step 4:

Q: What is the axis of symmetry for the equatiin: f(x)=2(x+1)^2+1

A: f(x)=2(x+1)2+1As a first step, we need to compare this equation with the equation of a parabola in…

Q: Given the function h, find functions f and g such that h(x) = (go f)(x). h(x) = (6+ 4x)" a. f(x) =…

A:

Q: Find domain and range of the * function y = Vx2 – 4x

A: To find the domain and range of  y=√(x²-4x)

Q: Find the domain and range of the function f(x)=√12-3x^2

A:

Q: If the point (-1/2, 1) is on the graph of f(x)=a(x-3)^2+50, what is the value of a?

A:

Q: (i) X= “ABCDBCDC” and Y=” BCDCD” (ii) X= “POLYNOMIAL” and Y= “ EXPONENTIAL”

A: This is a problem of counting and finite math.

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.