Answer:
- max for 5th-degree: 4 turns. This function: 2 turns.
- max for 7th-degree: 6 turns. This function: 0 turns.
Step-by-step explanation:
In general, the graph of an n-th degree function can make n-1 turns. However, in specific cases, the number of turns is limited by the number of real zero-crossings of the derivative.
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1. This 5th-degree function can have at most 4 turns. However, the derivative, f'(x) = 5x^4 -3, has only two (2) real zeros. Hence the graph of this function can only have 2 turns.
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2. This 7th-degree function can have at most 6 turns. However, the derivative, f'(x) = -7x^6 -35x^4-12x^2, has an even-multiplicity root at x=0 only. The derivative never crosses 0. Hence the graph makes no turns.
Step-by-step explanation:
V= π*r²*h
V/π = r²*h
v/(π*r²) = h
= 5
x+y = 15
x = 15-y
Answer:
Students should be able to find the x-intercepts of a quadratic function using both factoring and completing the square. All that should be given to students is the standard form of a quadratic equation in the form y = ax^2 + bx + c.
Step-by-step explanation:
2 apples in the partly filled tray, 11 tents are needed for all the children