Create a sequence of secant lines that can be used to approximate the value of the derivative at x =-1 Give your values of h and the slope of the secant line Now think about the derivative of f (x) = 2 Caution: The graph of the function f(x) = 2* is still depicted below. for that value of h. h slope of secant line You can approximate the value of the derivative at x= a by looking at the slopes of the secant lines very close to the input a. That is for small values of h, find the slope of the secant line on the interval [a, a +h]. 10 Create a seguence of secant lines that can be used to approximate the value of the derivative at x=0. Give your values of h and the slope of the secant line for that value of h. h slope of secant line Create a sequence of secant lines that can be used to approximate the value of the derivative at x=1. Give your values ofh and the slope of the secant line for that value of h. -4 -3 slope of secant 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.
![Create a sequence of secant lines that can be used to
approximate the value of the derivative at x =-1.
Give your values of h and the slope of the secant line
for that value of h.
Now think about the derivative of f (x) = 2
Caution: The graph of the function f(x) = 2* is still
depicted below.
h
slope of secant line
You can approximate the value of the derivative at
x= a by looking at the slopes of the secant lines very
close to the input a. That is for small values of h, find
the slope of the secant line on the interval [a, a + h]
10
Create a sequence of secant lines that can be used to
approximate the value of the derivative at x = 0. Give
your values of h and the slope of the secant line for that
value of h.
-8
h
slope of secant line
Create a sequence of secant lines that can be used to
approximate the value of the derivative at x = 1. Give
your values of h and the slope of the secant line for that
value of h.
-4
3
-2
-1
h
slope of secant line](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcd290171-d51e-400a-b1c3-79ef9b44d769%2Ff4574b35-c854-488a-81fb-f3ec58a07268%2Fcis44jj_processed.png&w=3840&q=75)
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