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levacccp [35]
3 years ago
14

100 POINTS!!

History
1 answer:
loris [4]3 years ago
7 0
The Gilded Age was a time in American history that received its name due to the huge fortunes it created for different citizens. During this era, robber barons became an integral part of society. Robber barons were individuals who became rich/dominant in a particular industry through business deals. Some examples of robber barons include John D. Rockefeller, Andrew Carnegie, and JP Morgan.

John D. Rockefeller represented the Gilded Age well during this time. His monopoly on the oil industry allowed him to be considered one of the richest people in American history. At one point, Rockefeller controlled roughly 90% of the oil consumed in the United States. This allowed Rockefeller to live a lavish lifestyle.

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What is the maximum number of turns for the graph of f(x)=x^4+3x^2?
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The turns of a graph is represented by the number of maximum or minimum that the function has.

If we differenciate f(x) we get:

f'(x)=4x^3+6x

f'(x)=2x(2x^2 + 3)

Therefore f'(x) =0, when x=0. Given that negative roots are not defined.

Therefore, the number of turns will be given by the number of solutions of f'(x) which is 1.

Attached you find the graph of the function which confirms the number of turns.

If the function had other solutions, the maximum number of turns it could have is 3! because f'(x) is a third degree polynomial, therefore it can't have more than 3 solutions!

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