Chapter2: Functions And Their Graphs
Section2.4: A Library Of Parent Functions
Problem 47E: During a nine-hour snowstorm, it snows at a rate of 1 inch per hour for the first 2 hours, at a rate...
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show that the polynomial below has a root between 0 and 1.
![The function given is:
\[ f(x) = 2x^3 - 11x^2 + 18x - 6 \]
This is a cubic polynomial function. Cubic functions are characterized by their general form \( ax^3 + bx^2 + cx + d \). In this particular function:
- The coefficient \( a = 2 \) indicates the leading term and influences the end behavior of the graph.
- \( b = -11 \) and \( c = 18 \) determine the shape and turning points.
- The constant \( d = -6 \) shifts the graph vertically.
Graphs of cubic functions typically have an "S" shaped curve and can have up to three real roots depending on the discriminant. They may intersect the x-axis at either one, two, or three distinct points. The maximum number of turning points for this function is two, corresponding to the changes in direction of the graph.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F99f990aa-ade1-4201-bad9-acb9a7debe3d%2Fb9d2968a-1cc7-4c1f-8e93-337ba8d7d4bb%2Fobo26q_processed.png&w=3840&q=75)
Transcribed Image Text:The function given is:
\[ f(x) = 2x^3 - 11x^2 + 18x - 6 \]
This is a cubic polynomial function. Cubic functions are characterized by their general form \( ax^3 + bx^2 + cx + d \). In this particular function:
- The coefficient \( a = 2 \) indicates the leading term and influences the end behavior of the graph.
- \( b = -11 \) and \( c = 18 \) determine the shape and turning points.
- The constant \( d = -6 \) shifts the graph vertically.
Graphs of cubic functions typically have an "S" shaped curve and can have up to three real roots depending on the discriminant. They may intersect the x-axis at either one, two, or three distinct points. The maximum number of turning points for this function is two, corresponding to the changes in direction of the graph.
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