For each lab, you must include an explanation of what you  did and how you did it. These must be typed and presented in an organized manner. The average slope formula is: [f(x2) - f(x1)] / [x2 - x1]   F(x^2) - It tells us the average slope over the interval from x1 to x2. Take the average slope of the function y (x) = x^2 + 3x +1 over one-unit intervals from 0 to 5. Graph the numbers (slopes), and what type of function do you see? Now repeat the process for g(x) = x^3.  take the slope of the slope and graph that for a hint.

Q: Determine where the graph of each function is concave upward and where it concave downward.  f(x)…

A:

Q: Find the x-intercept(s) of the following function. f(x)=x2−16

A: Just substitute f(x) equal to zero and solve the equation, you just need a2-b2=(a-b)(a+b).

Q: Graph by hand f(x)= -2tan(x/2) for x between 0 and 2pi. Show a table of values.

A:

Q: Use the graph of the given function f (x) to findf(1).

A: Given: Parabola graph is given.  Center (h,k) : ( 0 , -3)    Point: ( 1 , -1)

Q: nd the slope of the graph of the function f(x) - X X- 2 at x = 0.

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.