Consider the function fcx)=x t. Find the expression af the function lettwerd shitt gexl, Which represents three wnits and sketchit what functicn Would vepresents 2. downward shift by two units, Sketchiti 3 Fer the giuen functien fex) , wyte a hori Zntal 3. expression to represents an Shrinking by facter af 2 units en sketch it 3. Stretch the new function, computed in Part (a). ateng y-axis by facter af z untis and Sketch the function new.
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.
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Quiz/ class A
Consider the function fox)
t- Find the expression af the fuaction
lettward shitt
gexl, Which represents
three wnits and
sketchit
Wha
function would vepresents
a
downward shift By two units, Sketchit
Fer the giuen function fex),wyte
hori Zntal
expression to represents
an
Shrinking by
factor af 2 units
en
+Sketchit
3. Stretch the new function, computed
in part ta)
atong y-axis by
factor af z untis ound
functicn
SKetch the
new
Nete į Carsider te damain ef fex)
[^/-9]
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9:59 äclul 21.02.18](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1783d82a-15da-4287-a831-75f3d7f4a8d4%2F9259180d-af31-4236-a6b9-c8f05504bb71%2Fgwngyeb_processed.jpeg&w=3840&q=75)
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