Find the least squares approximation g(x) = a + a₁x + a₂x² of the function f, and use a graphing utility to graph f and g in the same viewing window. f(x) = 7x³, 0≤x≤1 (a) Find the least squares approximation g(x) = a₁ + a₁x + ₂x² of the function f. g(x) =

Q: Find the min and max of (f)

A: This question can be solved using the concept of maxima and minima.

Q: Consider two functions f(x) = 2x² + 16x + 6 g(x) = -8x² + 4x + 1. Let a be the maximum value of f(x)…

A: f(x)=-2x2+16x+6g(x)=-8x2+4x+1a is maximum value os f(x)+g(x)b the value of x at that…

Q: The maximum value of f(x) is 1+4x+x2

A:

Q: The Range of the quadratic function f(x) = -x² + 18x + 52 is O [-9, 00) O [52, 0) O (0,9] O (-∞0,…

A:

Q: The Range of the quadratic function f(x) = -x² + 15x + 45 is O (0,8] О -45, 8 O [-8, 0) O [45, 0) O…

A: By sketching the graph

Q: The Range of the quadratic function f(x) = -x² + 9x + 53 is O (0,4] O (-∞,53] O [53, ) O [-53, 4] O…

A: This question is based on finding range of quadratic function which is a downward opening parabola

Q: What is the maximum value  of the function f(x)= -x2 + 2x +1

A: f(x)= -x2 + 2x +1

Q: A Virginia Beach farmer has 480 acres of land on which to grow either corn or soybeans. He figures…

A:

Q: Find an equation in factored form for an even polynomial function with a local minimum at (2,0) and…

A:

Q: The figure shows the flow of traffic (in vehicles per hour) through a network of streets. X1 400-…

A: Given the figure shows the flow of traffic (in vehicles per hour) through a network of streets:…

Q: The Range of the quadratic function f(x) = -x² + 24x + 48 is, O [-48, 12]| о (), 12] O [48, 0) O…

A:

Q: Show that if the quadratic polynomial f (x) = x2 + rx + s takes on both positive and negative…

A: Find the real roots of the polynomial,

Q: Given (-1,12) is the maximum point for a quadratic function f(x) = 4h-(2k+x)²,where h and k are…

A: Given quadratic function is fx=4h-2k+x2

Q: The table shows projections for the female population of a country (in millions). Year Female…

A: The objectives are to  1) Estimate a quadratic function fx=ax2+bx+c that gives female population in…

Q: Suppose​ f(x) is a quadratic function such that its vertex lies on the​ x-axis. How many distinct…

A:

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.