Let's revisit the photo context, but this time we begin by resizing the photo by doubling the photo's width. We then crop (remove) 5 inches from the photo's width. Define a functionff that determines the resized photo's width (in inches), given the photo's original width, xx (in inches). f(x)=f(x)= syntax error Define a function gg that determines the cropped photo's width, gg(nn) (in inches), given the un-cropped width of the photo, nn (in inches). g(n)=g(n)= What is the resized and cropped photo's width (in inches) if the original photo was 21 inches wide? inches Use fuction notation to represent the value in (c), the resized and cropped photo's width, given the photo's original width is 21 inches long. (Your answer will look something like g(f(32))g(f(32)) or (f(g(19))(f(g(19)).) Define a function g∘fg∘f that combines the two processes (resizing followed by cropping) into one composite function. g(f(x))=g(f(x))=
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.
Let's revisit the photo context, but this time we begin by resizing the photo by doubling the photo's width. We then crop (remove) 5 inches from the photo's width.
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Define a functionff that determines the resized photo's width (in inches), given the photo's original width, xx (in inches).
f(x)=f(x)= syntax error
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Define a
function gg that determines the cropped photo's width, gg(nn) (in inches), given the un-cropped width of the photo, nn (in inches).g(n)=g(n)=
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What is the resized and cropped photo's width (in inches) if the original photo was 21 inches wide?
inches
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Use fuction notation to represent the value in (c), the resized and cropped photo's width, given the photo's original width is 21 inches long. (Your answer will look something like g(f(32))g(f(32)) or (f(g(19))(f(g(19)).)
-
Define a function g∘fg∘f that combines the two processes (resizing followed by cropping) into one composite function.
g(f(x))=g(f(x))=
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