Question Number 4: [CLO2, PLO1] Determine the concavity of the parabola representing the quadratic function, its y-intercept, its x- intercepts and the coordinates of the vertex. Also sketch the Parabola. f(x) = 10x²70x + 100 A. The demand function for a product is Q=f(p) = p² - 90p + 2025 ;0 ≤p ≤ 45 Where Q equals the number of units demanded and p equals the price per unit, stated in dollars. a) What type of function is this? b) How many units will be demanded at a price of $30? c) What price would result in zero demand for the product? B. Find the Distance, Slope and Midpoint of the line segment connecting (5,-10) and (15,-20). Also find the equation of this line.
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.
Q-4
Determine the concavity of the parabola representing the quadratic function, its y-intercept, its x-intercepts and the coordinates of the vertex. Also, sketch the Parabola.
- The demand function for a product is
Where Q equals the number of units demanded and p equals the price per unit, stated in dollars.
- What type of function is this?
- How many units will be demanded at a price of $30?
- What price would result in zero demand for the product?
![Question Number 4: [CLO2, PLO1]
Determine the concavity of the parabola representing the quadratic function, its y-intercept, its x-
intercepts and the coordinates of the vertex. Also sketch the Parabola.
f(x) = 10x? – 70x + 100
A. The demand function for a product is
Q = f(p) = p² – 90p + 2025
;0 <p< 45
Where Q equals the number of units demanded and p equals the price per unit, stated in dollars.
a) What type of function is this?
b) How many units will be demanded at a price of $30?
c) What price would result in zero demand for the product?
B. Find the Distance, Slope and Midpoint of the line segment connecting (5,-10) and (15,-20). Also
find the equation of this line.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0dece5d7-20ce-4eb0-8f10-0c0c764a3539%2Fb7efa99b-cfbf-4344-ad1a-11adced1d83c%2F4rhbmzr_processed.png&w=3840&q=75)
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